arXane › Physics › Condensed Matter
Wednesday, 4 November 2026: 14 new papers, 10 cross-lists and 18 replacements in Statistical Mechanics (cond-mat.stat-mech), in arXiv's order, with full abstracts. The same papers as arXiv's own listing, set as a newspaper; every title links to arXiv.
We study two restrictions of Baxter's symmetric twenty-vertex model on the triangular lattice, in which the three classes of vertices allowed by the ice rule carry the weights $a$, $b$ and $c$: chiral ice, in which only the twelve chiral vertices are allowed, and the model that excludes only the two alternating vertices. We show that neither model belongs to any of the known exactly solvable families of the twenty-vertex model, and we characterise chiral ice as the ice model in which every vertex has exactly one through line, a property that imposes a parity constraint along every closed lattice line. We compute the residual entropies of both models with transfer matrices on cylinders of up to twelve vertices in circumference, extrapolated with the finite-size correction predicted by conformal invariance, which we adapt to the triangular geometry and verify at two exactly solved points. The number of upward arrows crossing the cylinder is conserved, and the cost of changing it shows that both models are critical, with the long-distance behaviour of a free massless field. Chiral ice is the extreme point of a region of the phase diagram in which ordering had been suggested; along two paths through that region we find the same critical behaviour at every point, with no feature at the proposed boundary of the region. Along Baxter's exactly solved curve we obtain the corresponding exponents in closed form.
We consider the mean first-passage time $\tau(x)$ for an overdamped particle in a one-dimensional potential landscape, and address the problem inverse to the textbook one: Given $\tau(x)$ as a function of starting distance, we look for a potential that realizes it. We derive the conditions on $\tau(x)$ under which such a potential exists. We show that while the power-law dependences $\tau(x)\sim x^\alpha$ with $\alpha \leq 2$ may be realized by monotonic potentials, any realizable $\tau(x)$ with superquadratic growth requires potential wells arbitrarily far from the target; $\alpha = 2$ separates sliding from trapping-dominated motion regimes.
We investigate the phase diagram and nature of the phase transitions of three-dimensional compact lattice Abelian Higgs models with negative gauge coupling. These models describe multicomponent complex scalar fields coupled to a compact U(1) gauge field. Negative gauge coupling favors frustrated plaquette configurations, competing with the tendency of the matter ferromagnetic-like interaction to suppress frustration. Monte Carlo simulations and finite-size scaling analyses of models with one- and two-component scalar fields of unit charge reveal a substantially richer phase structure than at nonnegative gauge coupling. For two components, the O(3) transition line associated with gauge-invariant bilinear ordering extends into the negative-coupling region, and turns into a first-order transition line with decreasing $K$, toward the fully-frustrated $K\to -\infty$ limit. An analogous first-order transition line is also found for the one-component scalar matter with negative gauge coupling. Both one- and two-component models exhibit two additional continuous transition lines at sufficiently large matter coupling. Their energy-cumulant scaling is consistent with three-dimensional Ising and XY critical exponents, suggesting topological transitions in the $\mathbb Z_2$ and XY gauge universality classes, respectively. These results uncover additional phases generated by the competition between matter ordering and dynamical gauge frustration, whose physical characterization remains an open question.
The Thermodynamic Bethe Ansatz (TBA) procedure developed by Yang-Yang provides the free energy functional to be minimized via a variational problem. Their result not only gives the correct thermodynamics, but it also sets the framework for Generalized Hydrodynamics. Originally developed for quantum systems, this procedure has been recently successfully applied to (integrable) classical particle systems. However, this has never been done for classical field theories: no classical derivation has consistently accounted for solitons, breathers, radiation (dispersive modes), and their mutual interactions. We here derive the TBA equations for the Toda chain directly from its inverse scattering transform. This results in solitonic modes interacting with radiation, extending the soliton gas picture. We provide numerical verification of our equations against well established TBA equations in terms of particle modes. We expect the same procedure should apply to KdV, and pure radiative models as defocusing NLS and Sinh-Gordon, while we discuss current limitations in other models such as focusing NLS (and Ablowitz-Ladik) and Sine-Gordon.
The ubiquitous power-law relaxation emerges from complex mechanical systems with a vast number of interacting exponential responses. Here we demonstrate that power-law responses satisfy a maximum entropy criterion, regulating the individual contributions under partial knowledge. This leads to a prediction that frequency range of validity decreases with power-law exponent, a property which is confirmed for some biological materials. The close relation with the fractional standard linear solid also leads to an incorporation of the equally ubiquitous stretched exponential behavior.
Understanding how nonequilibrium systems evolve between distinct statistical regimes remains a fundamental challenge in statistical physics. Here we show that particle deposition at an evaporating contact line provides an experimental realization of cooperative one-dimensional deposition, in which post-deposition capillary attraction drives particles to migrate, cluster, and coarsen. As deposition proceeds, the cluster-width distribution undergoes a striking re-entrant transition, evolving from an initial exponential form to a peaked Gamma distribution and subsequently returning to an exponential form. This dynamic transition is accompanied by a non-monotonic crossover in fluctuation scaling, $\sigma_w\sim\langle w\rangle^\kappa$, with $\kappa$ changing successively from $1$ to $1/2$ and back to $1$. Monte Carlo simulations reproduce these statistical transitions. Our results establish evaporative contact-line deposition as a simple model of correlated one-dimensional assembly and reveal how local interactions can produce re-entrant statistical behaviour in a nonequilibrium system.
The two-dimensional Baxter-Wu model belongs to the universality class of the four-state Potts model. Exact expressions are available for its energy, specific heat, magnetization, and polarization amplitudes. We use these results as a benchmark for evaluating two simulation algorithms and two approaches to extracting critical amplitudes. Microcanonical population annealing (MCPA) and the sublattice-freezing Wolff algorithm yield highly consistent estimates for the energy and order parameters when applied to lattices of comparable size. According to the exact Joyce series, the local effective exponent does not stabilize at a constant value but instead undergoes a monotonic drift. This behaviour stems from corrections to scaling, which can be expressed as a series in the cube root of the reduced temperature. As a result, these corrections decay relatively slowly, with the leading term being of relative order $|t|^{2/3}$. When performing a fit with a free exponent on an automatically identified plateau, this drift gets incorporated into the estimated exponent, introducing a substantial bias in the derived amplitudes. In contrast, a fit that fixes the exponent to its exact value and explicitly accounts for the analytic correction series delivers a close match to the known exact amplitudes. Using this refined fitting approach, we obtain estimates for the susceptibility amplitudes and the universal amplitude ratios. These values are in good agreement with predictions from form-factor calculations. Additionally, we numerically determine the leading correction coefficient for the polarization.
Target search processes are often carried out by diffusive elements that are introduced and removed at random times, causing fluctuations in the number of searchers in the system over time. For instance, proteins are synthesized and degraded stochastically in the cell, and susceptible to react with specific binding sites during their lifetime. Here we derive the density profile generated by non-interacting particles subject to stochastic synthesis and degradation (SSD) at constant rates, given a source location and an arbitrary propagator for the single, non-degrading particle. We also study the first-passage properties of these many-searcher processes, which can be deduced from the knowledge of the first-passage time distribution of a single particle. We analyse the behaviours of the characteristic reaction time and of the mean first-passage time in the limits of small and large rates. Taking into account the costs associated with synthesis leads to the existence of an optimal synthesis rate. We further generalise these results to bursty synthesis, when production events involve more than one particle at a time, as often observed in cell biology. The mean first-passage time in these situations can be significantly reduced at low synthesis or large degradation rates, as it is divided by the mean burst size in these regimes. The results presented here are applied to one-dimensional Brownian searches. Some general connections between SSD and resetting processes are pointed out as well as important differences, since SSD is associated with a distinct queueing protocol.
For one-dimensional diffusion processes with arbitrary diffusion coefficient $D(x)$ and Ito force $F_I(x)$, we analyze the statistical properties of the renormalized trajectories at scale $\Gamma$, where one keeps only the alternating sequence of local minima and local maxima that are separated by drawups and drawdowns of amplitude bigger than $\Gamma$. The elementary RG-step between $\Gamma$ and $\Gamma+d \Gamma$ thus amounts to eliminate the drawups and drawdowns of amplitude $\Gamma$, a real-space-RG-procedure that is well-known for Brownian trajectories in the context of the Strong-Disorder-RG approach applied to the disorder landscape of random models. The main result is that the universality classes are determined by the scale function $s(x)$ satisfying $D(x) s''(x)+F_I(x) s'(x)=0$ that governs the exit probabilities from an interval : all the diffusions sharing the same scale function $s(x)$ have the same statistics of renormalized trajectories, even if their initial microscopic trajectories are completely different. The simplest universality classes for diffusions on the whole line $x \in ]-\infty,+\infty[$ and on the half-line $x \in ]0,+\infty[$ are illustrated with several examples of processes, with or without steady states: Cauchy, Student, Bessel, Fisher-Snedecor, Geometric Brownian. This framework concerning diffusion processes is then adapted to discrete-time and to continuous-time random walks on the one-dimensional lattice with arbitrary nearest-neighbor jump probabilities or rates.
Strong anomalous diffusion is often characterized by a piecewise-linear spectrum of the moments of displacement. The spectrum is characterized by the slopes $\theta$ and $\zeta$ for small and large moments, respectively, and by the crossover moment $q_c$ at which the slope changes. The exponents $\theta$ and $\zeta$ characterize the asymptotic scaling of the bulk and of the tails of the probability distribution function of displacements, respectively. Here, we adopt asymptotic theory to match the behaviors at intermediate scales. The resulting constraint explains how distributions with algebraic tails imply strong anomalous diffusion, and it relates $q_c$ to the corresponding power law. Our theory provides universal hyper-scaling relations between the exponents characterizing strong anomalous diffusion, and it yields explicit expressions for the leading-order corrections to the asymptotic power-law behavior of the moments of displacement. We also characterize finite-time corrections and propose a robust distribution-based method to estimate $\theta$, $\zeta$, and $q_c$. The findings are supported by numerical and analytical results for three paradigmatic models exhibiting strong anomalous diffusion. Finally, we show that power-law tails are not only sufficient but also necessary for this scenario: with a Gaussian, or generally fast-decaying, bulk and exponentially rare ballistic excursions, the spectrum of moments is single-linear, and the crossover to the apparent second branch drifts with the observation time. When the bulk is fast decaying and the tail is a power law, strong anomalous diffusion is still present, but the hyper-scaling relations among the exponents are violated.
We propose a weakly coupled description of the long-range transverse-field Ising chain near its short-range crossover at $s_*=7/4$, where the couplings decay as $r^{-1-s}$. The Ising conformal field theory is coupled to an instantaneous Gaussian field through $\sigma\chi$, extending the classical long-range Ising duality to quantum chains. The equal-time interaction generates a stress-tensor deformation that causes the velocity to run and renormalizes the dynamical critical exponent $z$. Conformal perturbation theory gives $z=1-0.720\,\delta+O(\delta^2)$, $1/\nu=(1+z)/2+O(\delta^2)$, and $\omega=\delta+O(\delta^2)$, with $\delta=s_*-s$. DMRG calculations on periodic chains of up to $128$ sites provide a consistency test using theoretical inputs for $1/\nu$ and $\omega$. After accounting for slow finite-size corrections, static and dynamical estimates of $z$ agree, supporting the crossover expansion at $s=1.5$ and a two-sided Pad\'e interpolation at $s=1$, $1.25$, and $1.5$.
We study $S=1$ compass models on the square and kagome lattices with bond-dependent bilinear and biquadratic interactions parametrized by an angle $\theta$. For compatible geometries, we determine the exact ground-state manifolds throughout the interval $\pi/4\leq\theta\leq3\pi/4$. At each endpoint, a product of on-site unitaries maps the Hamiltonian to the Laplacian of a configuration graph $\mathcal{G}$ in the $S=1$ Cartesian basis. These endpoints are exact Rokhsar-Kivelson (RK) points, with one ground state per dynamically connected component of $\mathcal{G}$. Each such state is an equal-amplitude superposition in the transformed basis and acquires configuration-dependent phases upon transforming back to the original basis. Both models possess $m=O(L)$ independent and mutually commuting conserved $\mathbb{Z}_2$ line charges, where $L$ is the linear system size, forcing a ground-state degeneracy of at least $2^m$ at the RK endpoints. Throughout the interior region, $\pi/4<\theta<3\pi/4$, the ground-state manifold on each lattice is instead spanned by two product states, both annihilated by the Hamiltonian. On both lattices, each RK endpoint also hosts a first-order transition into this intervening interior phase spanned by the two product states with long-range order.
Maximum-entropy models of neural recordings can be treated as Boltzmann distributions at a fictitious temperature $T$, with the fitted model at $T=1$. Their specific-heat peak grows with population size and approaches that temperature, which has been read as a sign of criticality. The case rests on pairwise models, yet retinal codes require higher-order interactions. The thermodynamics of a model with such interactions fitted cell by cell has not been computed. Here I compute it exactly for pairwise and third-order models of the same populations of up to $20$ retinal ganglion cells, in salamander and marmoset. The triplet terms, required by the held-out likelihood, shift the peak by more than the finite-sample bias, with opposite sign in the two retinas. The peak is lower and grows more slowly in salamander, higher and grows faster in marmoset, and lies closer to $T=1$ in both. An exact decomposition traces most of the shift to the energy variance across population spike counts. A constraint on the spike-count distribution alone reproduces all of it in salamander and over half in marmoset. A second recording of each species, re-binning, and a common-input surrogate show that the sign is set by the spike-count structure of a recording at its temporal resolution, not by species. The thermodynamic signature of a neural code is therefore set not by the data alone but by the interaction order of the model used to read it.
We investigate quantum error correction protocols for topological codes deformed away from their stabilizer limits, particularly as they are pushed towards quantum phase transitions into trivial phases. Our focus is primarily on quantum information stored within the ground-state manifold of the transverse-field toric code (TFTC), subjected to independent bit-flip and phase-flip decoherence. Although the transverse field induces strong quantum fluctuations of $m$ anyons in the ground states, we show that projective measurements of the "bare" toric code stabilizers can nevertheless be used to construct an efficient decoding algorithm which exhibits a finite threshold to both types of decoherence, even when the transverse field is tuned infinitesimally close to the quantum critical point. Our construction of the optimal postmeasurement decoders---that is, the optimal decoders assuming that the stabilizers are first measured---crucially relies on the stoquastic nature of the TFTC Hamiltonian, which affords a description of its ground states in terms of a classical lattice gauge theory. Using stoquasticity, we first prove that stabilizer measurements act unitarily on the undecohered TFTC ground states to excellent approximation, and that the optimal postmeasurement decoder can be efficiently implemented via Monte Carlo simulation of a constrained lattice gauge theory. We then construct the optimal postmeasurement decoder for the TFTC states under bit-flip and phase-flip decoherence, where we numerically demonstrate a finite threshold close to the quantum critical point. We provide theoretical evidence (without a rigorous proof) that stabilizer measurements constitute an optimal decoding strategy in this setting. For phase-flip decoherence, we further prove that the optimal postmeasurement decoding threshold is independent of the transverse field strength throughout the topological phase.
We show that, starting from the same state, optimal driving can sometimes reach a colder (or hotter) target in the same amount of time while dissipating less energy, or equivalently dissipate the same amount of energy in a shorter time. We study this counterintuitive phenomenon in the slow-driving regime of an open quantum system, where we name it Near-Equilibrium Anomalous Tradeoff (NEAT). We establish necessary conditions for its occurrence and show its underlying geometric origin. While NEAT is reminiscent of the well-known Mpemba effect, the two phenomena are distinct in general. We demonstrate NEAT in an exactly solvable qutrit model, as well as for d-dimensional birth-death dynamics with independently controlled energy levels. Finally, we show how NEAT can improve the performance of Carnot engines.
We find that coherent error can induce a phase transition from the clean surface code phase into an extended long-range entangled critical regime with diverging Markov length. To demonstrate this, we establish two general results of independent interest. The first relates topology and quantum information to mixed-state entanglement: we show that when a noise channel acting on a topological code preserves a higher-form symmetry and nonzero coherent information, the noisy state for generic logical input is long-range entangled. The second generalizes the local recovery construction based on finite Markov length to any locally parameterized family, thus encompassing local Lindbladian evolution, coherent errors followed by syndrome dephasing, and thermal states. We apply these results to the honeycomb surface code, in which we find an extended long-range entangled critical regime that is a quasi-long-ranged counterpart of 1-form strong-to-weak spontaneous symmetry breaking. As a byproduct of these studies, we relate the conditional mutual information to conductance in a Majorana network model.
Multiple seemingly distinct frameworks are commonly proposed to explain the emergence of effective non-Hermitian dynamics in quantum systems coupled to an environment. Furthermore, it remains contested how to properly calculate expectation values or whether thermal equilibrium states exist in non-Hermitian systems. In this work, we show that Feshbach projection, the Lindblad master equation, and the ancilla approach can all be understood through the Kraus map formalism, leading to non-Hermitian time evolution if an appropriate post-selection procedure is enforced. After first deriving an exact expression for the conditional system dynamics, we discuss the approximations employed in each approach and the classes of non-Hermitian Hamiltonians that can be obtained. Within this framework, we physically justify the consistency of the right-right formalism (as opposed to the biorthogonal one) for calculating expectation values. Finally, we demonstrate that the traditional notion of thermodynamic equilibrium is not applicable to general non-Hermitian systems. Consequently, stationary states are characterized as non-equilibrium steady states, which should not be conflated with system-projected thermal states of the system-environment composite.
A three-region junction in a free real relativistic scalar vacuum in $2+1$ dimensions yields a strictly negative logarithmic contribution to genuine tripartite R\'enyi multi-entropy for every integer $n\geq3$ and all nondegenerate sector angles. The replica subtraction exactly removes loop classes associated with a single interface. Surviving loops have positive, scale-independent weight, yielding a logarithm whose sign is fixed by the negative R\'enyi prefactor. The selector is empty at $n=2$. The flat-sheet Friedrichs prescription fixes the scalar operator at the nonmanifold replica apex. It yields a convergent angular spectral formula for the coefficient.
Topological defects are commonly characterized by their charge, although defects with the same charge can have different internal morphologies. We study the annihilation of isolated $\pm1$ defect pairs in a two-dimensional compressible Toner--Tu model, varying the morphology of the $+1$ defect while keeping the initial charges and separation fixed. Activity produces a morphology-dependent mobility asymmetry: reversing the radial orientation of an aster reverses which defect travels farther, and asters show the strongest response. An early-time analysis reveals that the initial morphology selects distinct density modes whose gradients subsequently feed back on the polarization. Consistently, removing the density-gradient coupling strongly suppresses the asymmetry. These results establish defect morphology, in addition to topological charge, as a dynamical variable governing defect-pair motion in active polar matter.
Mechanical disturbances such as seismic shaking can set a granular slope in motion. Understanding the resulting transport before arrest is important for predicting topographic change, assessing landslide hazards and controlling powder flows in industrial processes. Experiments show that smaller disturbances can trigger avalanches and larger areas are mobilized as slopes approach their stability limit. Yet how much transport varies between events under the same macroscopic conditions and forcing remains unclear. Here we use numerical simulations to show that transport variability is amplified near the critical angle. We apply identical basal pulses to static granular layers with the same macroscopic conditions but different initial particle configurations. Although the mean transport increases approximately in inverse proportion to the angular distance from the critical angle, the standard deviation increases even faster and can exceed the mean. Thus, identical forcing can produce widely different transport amounts. Deterministic constitutive laws that assign a unique response to given macroscopic conditions cannot capture this variability. We introduce fluctuations into the energy balance to develop a stochastic model that captures the main features of the broadening transport distribution. These results show that assessing transport near the critical angle requires considering its distribution, not just its mean, and motivate constitutive descriptions that incorporate fluctuations.
Ionic conduction in solid-state electrolytes is conventionally described by mobile cations migrating through a static host lattice. Yet the fastest conductors are often the most disordered, and how disorder enhances transport remains unresolved at the mesoscale, inaccessible to ensemble-averaged probes. We use Bragg X-ray photon correlation spectroscopy to measure nanoscale structural dynamics of a single ball-milled Na$_3$PS$_4$ particle. We find that the cubic phase behaves as a strain glass: a frustrated configuration of three degenerate tetragonal variants with short-range order. Its domain-wall motion is stress-driven, crossing over irreversibly to thermally activated dynamics on annealing as residual milling stress is depleted. Rearrangements follow scale-free avalanche statistics, matching ferroelastic martensites but without external driving. The tetragonal polymorph shows none of these features and relaxes fifty times more slowly. These dynamics occur on timescales comparable to estimated ionic diffusion across the particle, indicating the host structure cannot be assumed static on transport-relevant timescales.
Turbulence is defined by a set of emergent and singular phenomena: a constant-flux energy cascade, intermittency, a dissipation rate that survives the vanishing of viscosity, and the spontaneous loss of determinism of the inviscid limit. Which physical ingredients produce them remains unclear, because in fluids they always come together with incompressibility, spatial structure and vortex dynamics. Here we show that a hierarchy of inertia, coupled by the purely geometric nonlinearity of rigid constraints, is enough. A planar chain of rigid pendula whose lengths and masses decrease geometrically, coupled only through nearest-neighbor constraints, develops a far-from-equilibrium cascade that replaces thermal equipartition, with statistically local and time-irreversible energy transfer despite intrinsically nonlocal coupling. Its fluctuations are intermittent, yet self-similarity is restored by a hidden scale symmetry. As the viscosity vanishes, the dissipation rate saturates at a finite value, and thermal noise consistent with fluctuation-dissipation balance is amplified from the smallest to the largest scales within a fraction of a large-scale period. Because the hierarchy can be tuned and the same dynamics can be realized mechanically or electrically, turbulence becomes a property that can be designed and measured in the laboratory.
Quantum networks distribute entanglement between distant nodes by combining many short entangled links using local quantum operations. These operations only succeed probabilistically, yet existing percolation-based theories of entanglement transmission treat them as perfect. We approach the problem through statistical physics, using a stochastic generalization of concurrence percolation to determine how reliable local operations must be for long-range entanglement to remain possible. On hierarchical $(U,V)$-flower networks, which permit full analytical control across network scales, we derive an exact renormalization recursion for the probability that an end-to-end entangled connection survives. For the $(2,2)$-flower this yields a closed-form operational phase boundary, $\eta_p = 2 - \frac{32}{27}\eta_s$, where $\eta_s$ and $\eta_p$ are the success probabilities of the series (entanglement swapping) and parallel (purification) operations, respectively. At this boundary the survival probability jumps discontinuously from $0$ to $S_\infty = 3/(4\eta_s)$. Numerically propagating the full distribution of end-to-end concurrence yields a second threshold in the initial link quality, which varies continuously with operational reliability. Above both thresholds the large-network state is binary: the connection either fails outright or approaches a perfect Bell pair. Our results thus reveal a two-threshold structure for long-range entanglement, in which operational reliability and initial link quality can compensate one another. Operational success rates therefore emerge alongside initial link quality as a primary design constraint for scalable quantum networks.
Self-assembly enables complex structures to emerge from simple building blocks through local interaction rules. Are some structures intrinsically easier to design, that is, do they admit more sets of assembly rules than others? And, can this be predicted from their geometry? We address these questions using a three-dimensional polycube model with programmable face-to-face binding, defining a structure's assembly rule probability as the chance that a randomly chosen rule set produces it. For polycubes, this probability decreases exponentially with assembly complexity, the minimum information required to specify a structure's assembly rules. Intuitively, this follows because structures with low assembly complexity are generated not only by minimal rule sets but also by numerous more elaborate ones, and so arise disproportionately often. Symmetry can reduce assembly complexity by allowing the same building blocks and local interactions to be reused across different parts of a structure. Indeed, we find that the highest probability structures come from a tiny subset of highly symmetric structures. However, symmetry alone does not determine assembly complexity. Structures with the same symmetry can differ substantially in the amount of assembly information they require, depending on how effectively their global symmetry can be exploited by local growth rules. Overall, our results link information, symmetry, and assembly rule probability and suggest that identifying which geometric features permit rule reuse is central to designing minimal programmable self-assembling systems.