Papers

In this report, we have shown that, in an otherwise geometrically frustrated lattice, the underlying interactions compete to stabilize different magnetic phases. In conjunction with fluctuations, these interactions may lead to the formation of unusual ordered phases, providing a pathway for understanding the fluctuation-driven order-by-disorder phenomenon. This competition is further modified by the presence of inherent structural disorder in a frustrated two-dimensional lattice. Furthermore, due to the local nature of the additional structural disorder, the majority of the samples evolve toward glassy dynamics, which can not only mimic spin-liquid-like behavior but also make it difficult to identify genuine spin-liquid candidates experimentally.

We study low-$T$ transport and itinerant magnetism in 2D $\delta$-doped semiconductors. Large-scale Hartree-Fock calculations with random hoppings and repulsion $U_0$ reveal two transport regimes near a critical density. The conductivity $\sigma(T)$ initially increases as $T$ drops below $U_0 / 10$. However, at $T \sim U_0/100$, a tiny density of magnetic moments forms, driving an insulating downturn. Fractal wavefunctions locally amplify magnetic interactions, initially concentrating currents into branched filaments, but ultimately choking them off via dynamic SU(2) symmetry breaking.

In-context learning (ICL) allows a pretrained model to infer a new task from examples supplied in its prompt without updating its parameters. In linear models of ICL, the prediction error develops a double-descent singularity when the number of pretraining samples becomes comparable to the number of learnable parameters. We formulate this interpolation singularity as a critical phenomenon of a quenched disordered system. By comparing annealed and quenched descriptions of the same linear ICL model, we identify the connected sample-to-sample fluctuations of the learned parameters as the microscopic origin of the singular error. A Landau potential is constructed by integrating the cavity self-consistency equation for the renormalized ridge parameter $\xi$. The role of (magnetization) order parameter is played by $\xi$, while the bare ridge parameter $\lambda$ becomes its conjugate magnetic field. The normalized sample complexity $\tau$ acts as a temperature and the double-descent singularity occurs at the critical temperature $\tau_c =1$. The Landau susceptibility is precisely the quantity that diverges in the fluctuation contribution to the prediction error. The order parameter is closely related to the fraction of zero eigenvalues of the empirical relaxation matrix in the ridgeless limit, which define flat directions in the learning dynamics. The Landau theory is generically cubic in the order parameter with critical exponents $(\beta_{\rm cr},\delta_{\rm cr},\gamma_{\rm cr})=(1,2,1)$. In the large-context regime, there appears a pseudogap-like regime characterized by suppressed order parameter. Predictions of the Landau theory are independently confirmed from numerical solutions of the original learning problem with good quantitative agreement. Our results pave the way for solid statistical-physics understanding of the interpolation criticality in linear in-context learning.

Spectroscopy conventionally separates optical frequencies before detection, imposing persistent constraints on footprint, complexity and scalability. Here we establish an alternative paradigm in which the nonlinear optoelectronic dynamics of a single two-dimensional perovskite photodetector physically encode the incident optical field and machine learning performs the inverse spectral reconstruction. Using a planar fluorinated phenethylammonium lead iodide (F-PEAI) photodetector, we exploit wavelength- and irradiance-dependent current-voltage signatures arising from the coupled effects of photocarrier generation, trapping, interfacial transport and field-dependent carrier dynamics. A compact variational encoder-decoder preserves the functional and history-dependent structure of these responses by independently projecting forward and reverse voltage sweeps onto a truncated Legendre-polynomial basis before mapping them through a probabilistic latent representation to continuous spectral parameters. Trained on fewer than 400 experimental voltage sweeps, the model generalises to excitation wavelengths excluded from training, reconstructing wavelength with $R^2=0.958$ and a mean absolute error of 8.1 nm, while recovering log-normalised irradiance with $R^2=0.987$. Voltage-resolved analysis further reveals that wavelength and irradiance are encoded differently across the nonlinear device response, with distinct bias regions carrying complementary optical information. These results establish nonlinear material and interface dynamics as a computational resource for spectroscopy and point towards hardware-algorithm co-design in which materials, interfaces and inference architectures are engineered jointly to maximise information content, enabling compact spectroscopic systems without dispersive optics or detector arrays.

Efficient exploration of the complex potential-energy landscapes of amorphous materials is central to computational structure discovery and refinement. Conventional Monte Carlo, reverse Monte Carlo, and related methods typically sample configuration space through small, local trial moves and may require millions to tens of millions of moves to converge. Here, we evaluate larger, nonlocal perturbations followed by local geometry relaxation as an alternative sampling strategy. We develop and test four perturbation types using amorphous Al$_2$O$_3$ as a model system. Among them, moving an oxygen atom to change the coordination numbers of two aluminum atoms, allows access to low-energy configurations with substantially fewer trial moves than a conventional Monte Carlo trajectory. These results suggest that relaxation-assisted nonlocal moves could reduce trapping in local minima and improve sampling in structure-search and reverse Monte Carlo workflows.

The physics of information scrambling in quantum many-body systems is intimately related to thermalisation and emergence of chaos. However, its standard characterisation through bipartite entanglement or operator growth remains inherently coarse-grained, obscuring the spatiotemporal anatomy of how quantum information flows between different regions of the system and across various length scales. In this work, we develop a theory for the dynamics of local information in local random unitary circuits which resolves the fine-grained microscopic structures of local information flow in such systems. Using the framework of information lattice which systematises the information content at each length scale within each subsystem, we identify a distribution of length scales at which information resides and obtain the dynamics of the distribution. For Haar-random circuits with infinite local Hilbert-space dimensions, we map this dynamics onto an exact classical stochastic process which reveals that this distribution is described by a Tracy-Widom form which moves ballistically in time ($ \propto t$) toward larger scales, accompanied by a $\sim t^{1/3}$ broadening. We also find the same qualitative behaviour for random Clifford circuits acting on qubits. The similar scaling behaviour in two rather different settings hints strongly towards the universality of our results. In the case of Clifford circuits, we develop a phenomenological Markov process for the dynamics of the stabiliser generators in a specific gauge which confirms the Tracy-Widom distribution and the $t^{1/3}$ scaling of the fluctuations. Ultimately, our results establish the universal properties of the dynamics of local quantum information in a length scale-resolved fashion and provide a possible route towards bridging exact microscopic theories for information dynamics with emergent hydrodynamic descriptions of information flow.

Krylov and Lanczos approximations are used in quantum dynamics, quantum subspace methods, and Hamiltonian learning. A practical question is how long an $m$-dimensional Krylov truncation can be trusted. We argue that this time is fixed by causal propagation on the associated Jacobi chain. The relevant distance is not the Krylov index itself, but the inhomogeneous transport metric $\rho(m,n) = \sum_{j=\min(m,n)}^{\max(m,n)-1} 1/b_j$, where $b_j$ is the Lanczos hopping across the bond $j \leftrightarrow j+1$. We prove a Lieb–Robinson bound in this metric. Its small-weight limit gives the velocity $v_{\rm LR} = 2$, meaning that propagation is exponentially suppressed outside the cone $\rho(m,n) \simeq 2|t|$. The error of a finite Krylov approximation to the return amplitude is a round-trip effect: information has to travel from the probe to the truncation boundary and back. Combining the Lieb–Robinson bound with Duhamel's formula yields a lower bound on the error of the truncated dynamics. For a fixed tolerance $\epsilon$, let the break time $t_\ast(m;\epsilon)$ denote the longest time for which the $m$-dimensional truncation is guaranteed to reproduce the exact return amplitude within error $\epsilon$. We show that $t_\ast(m;\epsilon) \ge \tau_m[1-o(1)]$, where $\tau_m = \rho(0,m) = \sum_{j<m} 1/b_j$. When the probe spreads along the chain, this lower bound is also tight, so $t_\ast(m) \simeq \tau_m$. The situation is different when the probe excites only a localized part of the spectrum, or a part already resolved by the truncation. In this case, essentially no signal reaches the boundary. Beyond a state-dependent Krylov dimension $m_\ast$, the approximation can therefore remain accurate at all times, and the break time is effectively infinite. Numerical tests on spin chains and random Jacobi matrices support $t_\ast(m) \simeq \tau_m$ in the transport-limited regime.

We establish a sharp phase transition for fitting random vectors by an ellipsoid. The random vectors have independent subgaussian coordinates with mean zero, variance one, and a common fourth moment, and the number of vectors is proportional to the square of the dimension. We identify an explicit satisfiability threshold such that, with high probability, a positive definite ellipsoid passes through every data point below the threshold, whereas no positive semidefinite fit exists above it. We also determine the optimal squared fitting error throughout the unsatisfiable regime. In particular, the threshold depends on the coordinate distributions only through their common fourth moment, revealing a fourth moment universality phenomenon. For standard Gaussian data the threshold is $1/4$, resolving the ellipsoid fitting conjecture.

The interplay between geometric frustration, spin–orbit coupling, and structural disorder can give rise to unconventional magnetic ground states in rare-earth triangular-lattice magnets. We report low-temperature magnetic and $^7$Li NMR investigations of the disordered triangular-lattice compound LiCaYb$_5$(BO$_3$)$_6$ (LCYBO). Rietveld refinement confirms a hexagonal $P6_522$ structure with partial Ca/Yb antisite disorder and fractional Li occupancy. Magnetic susceptibility and magnetization measurements indicate a well-isolated effective $J_{\mathrm{eff}}=1/2$ Kramers doublet with weak antiferromagnetic interactions ($\theta_{\mathrm{CW}} \approx -0.54$~K). The specific heat reveals a weak anomaly near 0.43 K, suggesting the development of short-range correlated magnetism rather than conventional long-range order. $^7$Li NMR spectra broaden strongly upon cooling, consistent with increasingly inhomogeneous internal magnetic fields. The spin-lattice relaxation exhibits two relaxation components consistent with disorder-induced distributions of local magnetic environments arising from antisite disorder and competing exchange pathways. Our results establish LCYBO as a structurally disordered frustrated triangular-lattice magnet with correlated low-energy spin dynamics.

Machine learning offers a possible route to data-driven real-space renormalization when the relevant observables are nonlocal and difficult to prescribe explicitly. We explore this idea for two-dimensional site percolation developping a supervised, scale-shared neural architecture. The model recursively applies the same learned coarse-graining rule across scales, producing a latent field from which the crossing probability is predicted, while a corresponding fine-graining decoder reconstructs the largest-cluster mask. Trained only on small lattices, the model extrapolates to substantially larger systems, recovers the spanning cluster with high fidelity, and produces observables obeying the expected finite-size scaling near the critical point. We observe that to get such performance it is key that the learned latent representation exhibits critical fluctuations and scale-dependent flows consistent with the renormalization-group structure of percolation.

A looped transformer performs inference by iterating a weight-tied map, making its computation a dynamical process whose cost is set by the resulting inference dynamics. Here we show that networks with identical architecture and objective, trained to identical accuracy, nevertheless realize distinct dynamical phases depending strongly on initialization, and that the bifurcation defining each phase determines how test-time compute scales. The phases are distinguished by their bifurcation mechanisms, including a saddle-node fold and a Neimark-Sacker-type transition to bounded nonstationary motion. In the fold phase, a one-dimensional normal-form reduction predicts both the relaxation-time and spectral-gap amplitudes from local derivatives of the trained map, yielding the parameter-free relation $\tau(\varepsilon)[1-\lambda_{\max}(-\varepsilon)]\to\pi$. Composed with a regular distribution of problem difficulty, the same critical slowing down produces the workload-level tail $P(\tau>N)\sim N^{-2}$. In the Neimark–Sacker phase, the fold scaling law disappears rather than merely changing its prefactor. Thus, test-time compute is not determined by architecture alone. It is governed by the dynamical phase of the solution found by training.

We investigate random recursive simplicial complexes growing by adding, at each step, a vertex together with a simplex formed by joining the new vertex with a randomly chosen existing simplex. We also add all faces of the new simplex to ensure that the resulting object remains a simplicial complex. If the choice of an existing simplex is uniform among simplices of dimension $<m$, the number $S_d$ of simplices of any admissible dimension $d\leq m$ is an asymptotically self-averaging random variable. This feature allows us to determine the asymptotic growth law of the average of $S_d$ when the number of vertices diverges. We also probe the degree distribution, examine the probabilities of various extreme outcomes, and analyze the characteristics of the first vertex.

We study an assembly of $N$ scalar fields coupled via a quenched random interaction, equivalent to a spin glass whose spins are promoted to $d$-dimensional fields. When $N$ is large, the random coupling matrix produces a family of Gaussian universality classes whose critical exponents are determined by the behavior of the eigenvalue density near the spectral edge. For a Wigner matrix, the correlation length diverges at criticality but the susceptibility remains finite, and one-loop replica analysis supports an upper critical dimension of unity. In an exactly solvable spherical variant, the heat capacity jumps at the transition in $d>1$, and correlations remain pinned to their critical form throughout the glass phase, giving generic scale invariance despite the absence of a Goldstone mode.

Structural color arises from the interaction of light with nanoscale structures and is widespread in nature. As structural complexity increases, the mechanisms governing coloration become progressively less understood. The optical response of periodic photonic crystals with a spatially periodic refractive index is well described by Bloch theory, whereas that of photonic glasses composed of randomly assembled uniform spheres is more subtle yet well studied. In contrast, disordered photonic networks found in many beetles are among the most complex natural photonic architectures, and the fundamental relationships between their structure and color remain unclear. Here, we use an inverse method to identify the structural features encoded in the reflectance spectrum. By comparing the spectrum of an unknown system with a database of simulated spectra from computer-generated photonic networks, we infer its structural properties. Applying this approach to both simulated networks and the biophotonic network responsible for the blue coloration of the weevil Pachyrhynchus congestus mirabilis, we identify rings and pores as the key local scattering motifs. Their characteristic sizes govern the spectral position of the reflectance peak, whereas short-range disorder controls its width. The inverse method reveals clear spectral signatures of short-range order, whereas the influence of hyperuniformity and primitive similarity appears comparatively weak. This suggests that blue structural coloration is governed by local scattering mechanisms rather than photonic band-gap effects. We propose an analogy to an inverse photonic glass, in which pores and rings act as correlated local resonators. This perspective provides new design principles for bio-inspired structural-color materials.

We study the localization of a quantum particle in a one-dimensional disordered system with long-range hopping amplitudes $t(r)\propto r^{-a}$. In contrast to the standard one-dimensional Anderson model ($a\to\infty$), in which all states are localized and the localization length is minimal at the band edge, the long-range model with $1<a<3/2$ exhibits a disorder-driven transition at the band edge, while high-energy states remain localized at arbitrary disorder strength. We investigate this transition for the ground state in momentum space. In the weak-disorder regime, we derive perturbative expressions for the characteristic functions and moments of the momentum-space wave function, as well as for its fractal dimensions. Our results demonstrate that the ground state exhibits $\it semilocalization$ rather than conventional localization, thereby extending the class of models displaying the unusual $\it semifractality$ of wave functions.

Continuous-time Markov chains (CTMCs) provide the backbone for modeling discrete stochastic dynamics across applied, physical, and biological sciences. Their integration with modern gradient-based machine learning, however, is limited by the hard categorical event selection intrinsic to Gillespie-type simulation algorithms. We exploit the affine state update to obtain the exact one-step conditional-mean sensitivity by differentiating normalized reaction propensities. We pair this backward rule with exact forward trajectories to define the propensity straight-through (PST) estimator. At the trajectory level, we show that one-step sensitivities composed across events can depart from the exact multistep sensitivity. We derive the resulting per-step discrepancy in closed form and prove that it vanishes identically for affine downstream dependence. PST matches the accuracy of Gumbel-Softmax straight-through across all benchmarks: reversible dimerization (0.06% error), a genetic oscillator (1.7% error), a 50-task repressilator suite (0.17% median error), and patch-clamp ion-channel recordings ($R^2$ = 0.988). Under matched settings, PST converges 3.0-fold faster on the oscillator and 2.1-fold faster on the ion channel. At deep-learning scale, PST trains a 203,796-parameter stochastic reaction network with hard sampling, reaching 98.22% MNIST digit classification accuracy. By differentiating an exact conditional mean rather than a relaxed sample, PST offers a temperature- and Gumbel-free path to scalable gradient-based learning through exact stochastic trajectories.

The simple exclusion process (SEP) is a paradigmatic model for nonequilibrium transport, yet its rich dynamics over an exponentially large configuration space remain notoriously intractable. Here, we leverage variational autoregressive networks to characterize the nonequilibrium dynamics of the symmetric (SSEP), asymmetric (ASEP), and totally asymmetric (TASEP) cases in one to three dimensions at any time. We validate the approach against established finite-time 1D and long-time 2D results for the SSEP, and further provide new results on dynamical activity, density fields and nonequilibrium phase transitions for 2D and 3D cases. In 2D, we give a directional-density criterion connecting the bulk-density organization to the 1D TASEP phase diagram, and reveal how boundary and bulk rates separately control the activity and susceptibility. In 3D, we provide the first finite-time characterization of the SSEP active-inactive phase transition, and uncover scaling relations over time. Across dimensions, the critical field follows a trend $s_c\sim L^{-2}$, suggesting tuning strategies by the characteristic diffusive length scale. Overall, this work establishes a unified neural-network framework for characterizing nonequilibrium dynamics of representative transport systems.

Hypergraphs describe higher-order interactions that involve more than a pair of nodes. A characteristic feature of hypergraphs is that their robustness can be strongly affected by the different roles of the nodes. Indeed, some nodes might be essential for a hyperedge's function, while others might not be. The loss of a single essential node completely destroys the hyperedge it belongs to, while the loss of a non-essential node has a buffering effect, inducing the hyperedge to simply reduce its size. In order to capture this phenomenology, we formulate a comprehensive theoretical framework for $(k,n)$-core percolation models on hypergraphs, where each node of a hyperedge is an anchor with probability $\theta$, and a hyperedge fails if an anchor node fails. Hypergraph $(k,n)$-core percolation problems can be classified as first-neighbor and second-neighbor problems, indicating that in the pruning process the connectivity is ensured only by the state of the first neighbors or the second neighbors, respectively. We derive self-consistency equations for first-neighbor and second-neighbor (node- and hyperedge-based) pruning processes, and obtain the size of the giant $(k,n)$-core. We obtain the phase diagram, including continuous and discontinuous transitions, and confirm our theory on random hypergraphs using numerical simulations. The results show how the heterogeneity of the nodes' functional roles and the extended range of the interactions affect the robustness of higher-order networks.

We perform a theoretical study of defect states within the photonic band gap of three-dimensional diamond crystals composed of point scatterers and doped with substitutional defects. The defects introduce localized states inside the photonic band gap, whose existence conditions and eigenfrequencies are expressed in terms of the on-site Green's function of the ideal defect-free crystal. Off-site Green's functions are also calculated as function of distance and are shown to vanish within approximately two unit cells. Finite-size effects are analyzed by comparing the results obtained in the infinite-crystal limit with numerical simulations based on the coupled-dipole method. The latter not only reproduce the eigenfrequencies of the defect states within the band gap, but also provide their lifetimes originating from the finite crystal size. The lifetimes of the defect states increase exponentially with crystal size, becoming very long for large crystals. In addition to defect states in the three-dimensional photonic band gap, the defects also give rise to strongly detuned states outside the gap, which decouple from the spectrum of the ideal defect-free crystal.

The idea that information processing is optimised near the boundary between order and chaos has emerged as a recurring principle across neuroscience, complex systems, and machine learning. Here we test this hypothesis in quantum many-body systems, numerically simulating two-dimensional Ising networks of up to $N=20$ spins, operated as quantum reservoirs for time-series forecasting. Using out-of-time-order correlators (OTOCs), we locate the onset of information scrambling as the input strength is swept, separating regimes where information is frozen and scrambled across the whole reservoir state. We show that prediction precision peaks at the onset of scrambling, along with the number of computational-basis states that the reservoir actively populates. We then show that prediction precision grows as a power law $\sim N^{\alpha}$ in the reservoir size, superextensively $(\alpha>1)$ at the onset of scrambling and only sublinearly $(\alpha<1)$ in either neighbouring regime. Finally, we show that scrambling enhances the nonlinear components of the reservoir memory while reducing its linear capacity. At the onset, the total memory capacity grows superextensively, provided that the necessary “forgetting” mechanism is supplied by a collective relaxation channel. These results consolidate the role of information scrambling in learning systems, turning it from an operating point into a scaling law for the performance of quantum reservoirs.

Oscillatory neural networks have been successfully applied to a number of computing problems, such as associative memories and computationally hard optimization tasks. In this paper, we show how to use oscillators to process time-dependent waveforms with minimal or no preprocessing. Since preprocessing and first-layer processing are often the most power-hungry steps in neural networks, our findings may open new doors to simple and power-efficient edge-AI devices.

The entropy production rate (EPR) quantifies irreversibility of a nonequilibrium steady state, yet standard formulas obscure how a complex interaction network generates it. For multivariate Ornstein-Uhlenbeck dynamics on such networks, we express the EPR as a quadratic form in antisymmetric matrices measuring the nonreciprocity of aggregate directed walks at every length, and, equivalently, as two weighted-walk quantities: pairs of directed walks sharing both endpoints, and directed closed walks. For diagonalizable interactions, an exact correspondence translates these walk quantities into eigenvalues and biorthogonal eigenvector overlaps. Across dense, sparse, and deep acyclic random interactions satisfying matched-walk conditions, the mean EPR per node universally follows the square-root law $\phi_*(g)=1-\sqrt{1-g^2}$, where $g \in [0,1)$ parametrizes the interaction strength. Deep acyclic interaction matrices are nilpotent, with all eigenvalues fixed at zero for every $g$, yet, as their depth increases, their mean EPR per node approaches $\phi_*(g)$. Thus, the square-root law arises from directed walk properties, rather than from a shared spectral density or specific network topology.

The design of disordered point patterns with desirable properties is an exciting and ongoing research endeavor, with applications ranging from materials to computer science. A successful approach in recent years has been the optimization of point patterns through a loss function that enforces properties in their Fourier-space representation. Yet, these methods have so far strictly been limited to flat Euclidean space, precluding their use in the contexts of coatings of curved surfaces for photonics, or of sampling of curved manifolds for instance. We introduce FaSHIoNPOp, an algorithm that relies on fast non-uniform spherical harmonics transforms, to enforce pair correlations in point patterns on the sphere with an $O(N \log N)$ complexity in $N$ the number of points. Having demonstrated its performance, we showcase applications of FaSHIoNPOp, ranging from the generation of hyperuniform structures on the sphere for sampling and physical applications, to the design of gyromorphs (disordered structures with maximal scattering power at a given frequency) on the sphere. We additionally show that FaSHIoNPOp can be combined to both global constraints like centrosymmetry, with applications to the design of more isotropic $3d$ gyromorphs, and local real-space constraints like pair repulsion. Our work paves the way for optimal sampling and coating design on curved manifolds, with many applications across physics, materials and computer science.

We study how non-magnetic impurity scattering affects the emergence and possible coexistence of pairing instabilities in a two-node multi-Weyl semimetal. Within an explicitly specified projected impurity kernel—valley diagonal and momentum independent across each Fermi pocket, the leading behaviour of non-magnetic disorder in the small-pocket window $q^{\max}_{\rm intra}\xi_{\rm dis}\ll1\ll|2\mathbf Q|\xi_{\rm dis}$, treated at leading order in Born and Abrikosov–Gor'kov theory—quenched disorder tunes the leading pairing instability from a topologically nontrivial monopole channel to a conventional ($s$-wave) one, extending our earlier clean-system analysis into the disordered regime. A Born self-energy calculation in the chiral band basis then gives: (i) a band-isotropic conventional channel that is Anderson protected against intra-node scalar disorder ($\eta_s=1$), introduced phenomenologically at the projected-band level; solving the competition for arbitrary $\eta_s$ yields the crossing criterion $(1-\eta_s)/(1-\eta_m)<T_{c0}^{(s)}/T_{c0}^{(m)}$, so the mechanism tolerates substantial loss of conventional-channel protection; and (ii) a rank-one monopole sector fixing $f_m$ as the exact eigenfunction with $\eta_m(J)=1/(J+2)$, exact given that kernel. The crossing location in $\Gamma_N/T_{c0}^{(m)}$ is set by $\eta_m(J)$, $\eta_s$, and $r=T_{c0}^{(s)}/T_{c0}^{(m)}$. From the clean projected BdG Hamiltonian the pure monopole nodes carry Berry charge $\pm J$, distinct from the gapped conventional solution; the clean nodal thermodynamics is charge-dependent, $N_{\rm SC}(E)\propto E^{2/J}$ and $C\propto T^{1+2/J}$, and the residual density of states shows a threshold only for $J=1$. The crossing lies in the moderately metallic regime, $\mu/\Gamma_N\simeq11$–$14$ for the illustrative $T_{c0}^{(m)}/\mu=0.133$ used in the figures.

Within a cluster extension of the coherent potential approximation, disorder averaging generates a non-local self-energy that renormalizes both diagonal and off-diagonal hopping terms of the non-interacting Kagome-lattice Hamiltonian. These renormalizations (of both nearest- and next-nearest-neighbor hopping amplitudes) drive the system between two topologically trivial insulating states through an intermediate gapless phase characterized by conducting edge modes over a broad range of impurity concentrations. Our results demonstrate that multiple-scattering effects alone can generate emergent effective spin-orbit interactions and qualitatively modify the edge spectrum of disordered Kagome systems.

Exact sampling from the Boltzmann distribution of spin glasses remains an outstanding challenge: Markov chain Monte Carlo methods suffer from critical slowing down and metastable trapping, while modern neural autoregressive samplers such as variational autoregressive networks are approximate and, in the absence of exact reference samples, cannot be rigorously benchmarked. Here we present an exact autoregressive sampling algorithm for planar Ising spin glasses based on the Kac–Ward theory. Under the chain-rule factorization, sequentially fixing spins induces boundary-localized external fields, which destroy the zero-field structure required for exact evaluation. By encoding these fields with a planarity-preserving auxiliary spin construction, the conditional partition functions are mapped to an extended zero-field Ising model and exactly evaluated using the Kac–Ward determinant formula. The method generates strictly independent and identically distributed samples with exact normalized likelihoods at a computational cost of $\mathcal{O}(N^{5/2})$ for $N$ spins, thereby providing an exact baseline for benchmarking neural autoregressive samplers.

We study boundary free energies and half-space responses in nearest-neighbor disordered Ising models. First, we prove the existence of fixed-depth tangential pressure and identify its derivative almost everywhere with the limiting boundary response. Second, under quenched exponential boundary-response mixing, we prove Gibbs-state selection independence and exponential convergence of finite-depth pressures. We further show that uniform one-spin mixing yields DLR uniqueness and Gaussian normal localization, and verify the required mixing conditions whenever $(2d-1)\mathbb E\tanh(\beta\vert{}J\vert{})<1$. Finally, we establish an all-face surface limit in the bounded Dobrushin regime and provide counterexamples that delimit general surface and stiffness claims.

The critical exponents and universality classes of localization transitions in quasiperiodic systems are of fundamental importance for understanding critical phenomena in aperiodic systems. Here we show that the dynamical critical behavior can be tuned without adding new terms or changing the form of the Hamiltonian, but solely by varying the incommensurate frequency of the quasiperiodic onsite potential. We construct a family of incommensurate frequencies from the limiting ratios of generalized Fibonacci sequences controlled by the parameters $(m,n)$, and use them to define the quasiperiodic onsite potential. By combining generalized fidelity susceptibility, localization-length scaling, and finite-size gap analysis, we find that the correlation-length exponent is insensitive to the choice of the incommensurate frequency and remains consistent with the correlation-length critical exponent, $\nu \simeq 1$, in the localization transition of the standard Aubry–Andr'e–Harper model. In contrast, the dynamical exponent extracted from the low-energy gap scaling varies systematically with the incommensurate frequency. Our results show that changing the incommensurate frequency provides a simple way to tune dynamical critical scaling in deterministic aperiodic systems. Our results suggest instead that the arithmetic structure of an irrational number can serve as a control parameter for nonequilibrium quantum dynamics, enabling the tuning of dynamical critical behavior without changing the microscopic Hamiltonian or the physical spatial dimension.

Reentrant transitions and temperature chaos are two unusual properties of spin glasses. We recently established a general logical relation between these two phenomena [Phys. Rev. E 112, 044140 (2025)]. In the present paper, we provide an explicit example of this logical relation in the fully connected Ising $p$-spin glass with a ferromagnetic bias. By expanding the free energy around the triple point, we show analytically that the ferromagnetic–spin glass boundary is reentrant in the vicinity of the triple point throughout the examined range of finite $p>2$. It then follows from the above logical relation that there exists at least one pair of distinct temperatures in the spin glass phase for which the overlap of spin configurations vanishes. This is a necessary condition for temperature chaos, but it would be quite unusual for the overlap to vanish only for selected temperature pairs but not for others within a single spin glass phase. These results therefore strongly suggest the existence of temperature chaos in the sense that the overlaps of spin configurations vanish for all temperature pairs throughout the spin glass phase. Independent evidence for this behavior is provided by a two-temperature replica calculation.

Biological and artificial networks compute by transforming time-dependent inputs into functional outputs. Because the internal state of a stochastic network relaxes on finite timescales, its output generally lags behind a changing environment, producing computational errors. We show that for reversible continuous-time Markov networks the error admits a universal thermodynamic bound. Decomposing the total error into representation and lag contributions, we derive an inequality relating the lag error to the entropy production rate and a memory time equal to the integrated equilibrium autocorrelation of the output observable. The bound implies that accurate dynamical computation requires either substantial dissipation or long-lived memory encoded in slowly relaxing modes. We demonstrate these principles in artificial Markov networks and in models of biochemical information processing. Our results establish a thermodynamic limit on information processing in stochastic networks and provide a quantitative framework for understanding the energetic costs of biological computation.