arXiv subjects

Hai-Jun Zhou

Publications and source records attributed to Hai-Jun Zhou.

At least 19 recordsLinked to original sources

arXiv2026

Spontaneous symmetry-breaking in equilibrium tree-packing configurations of a kinetically constrained cubic-lattice system

We explore kinetic-constraint induced thermodynamic phase transition in the cubic lattice, employing the Fredrikson-Anderson spin model with hyperparameter $K=2$ as a representative kinetic system. Each lattice site may flip its binary occupation state if at most one of its six nearest neighbors is currently occupied. The whole set of microscopic configurations that are kinetically connected with the fully empty one is described by an equilibrium partition function with a single global constraint, that is, the occupied sites do not form closed loops but instead organize into different tree components in the lattice. We discover a continuous thermodynamic gas--crystal phase transition in the cubic system and determine the critical chemical potential $μ^* \approx -3.252$, at which the occupied sites of the equilibrium tree-packing configurations start to prefer one of the two nested cubic sublattices. This thermodynamic phase transition is absent in the two-dimensional square lattice.

cond-mat.stat-mech↗

arXiv2026

Thermodynamic phase transitions in lattice spin systems with severe kinetic constraints: Numerical simulation results

The Fredrickson-Andersen model with hyperparameter $K=1$ is a severely constrained kinetic lattice spin system, such that any site is temporarily blocked from changing its packing state (empty or occupied) if there is one or more occupied nearest neighbors. Starting from a completely random initial configuration with a fraction $ρ$ of sites being occupied, some of the sites may be permanently frozen to their initial state under this severe kinetic constraint. The remaining sites can switch states at least occasionally, and they form the unfrozen subsystem associated with the given initial configuration. In the present work we investigate thermodynamic phase transitions in such unfrozen subsystems of the two-dimensional square lattice and the three-dimensional cubic lattice by extensive numerical simulations. We demonstrate that the giant connected component of the unfrozen subsystem collapses at certain critical value $ρ_{c}$ of initial packing density, with $ρ_c = 0.2475$ for the square lattice and $ρ_c = 0.2809$ for the cubic lattice. This phase transition belongs to the same universality class of the conventional site percolation. We also observe that the ground states (densest packing configurations) experience a continuous crystal-to-glass phase transition at the critical value $ρ^* = 0.1423$ of initial packing density for the cubic lattice. For the two-dimensional square lattice we argue that long-range crystalline order is destroyed in the ground states as long as the initial packing density $ρ$ is positive.

cond-mat.stat-mech↗

arXiv2026

Response time of lateral predictive coding and benefits of modular structures

Lateral predictive coding (LPC) is a simple theoretical framework to appreciate feature detection in biological neural circuits. Recent theoretical work [Huang et al., Phys.Rev.E 112, 034304 (2025)] has successfully constructed optimal LPC networks capable of extracting non-Gaussian hidden input features by imposing the tradeoff between energetic cost and information robustness, but the resulting dynamical systems of recurrent interactions can be very slow in responding to external inputs. We investigate response-time reduction in the present paper. We find that the characteristic response time of the LPC system can be minimized to closely approaching the lower-bound value without compromising the mean predictive error (energetic cost) and the information robustness of signal transmission. We further demonstrate that optimal LPC networks taking a modular structural organization with extensively reduced number of lateral interactions are equally excellent as all-to-all completely connected networks, in terms of feature detection performance, response time, energetic cost and information robustness.

q-bio.NC↗

arXiv2025

Discontinuous phase transition of feature detection in lateral predictive coding

The brain may adopt the strategy of lateral predictive coding (LPC) to construct optimal internal representations for salient features in input sensory signals, reducing the energetic cost of information transmission. Here we first consider the task of detecting one non-Gaussian signal by LPC from Gaussian background signals of the same magnitude, which is intractable by principal component decomposition. We study the emergence of feature detection function from the perspective of tradeoff between energetic cost $E$ and information robustness, and implement this tradeoff by a thermodynamic free energy. We define $E$ as the mean $L_1$-norm of the internal state vectors, and quantify the level of information robustness by an entropy measure $S$. There are at least three types of optimal LPC matrices, one type with very weak synaptic weights and $S \approx 0$, and two functional types either with low energy $E$ or with high entropy $S$ in which one single unit selectively responds to the non-Gaussian input feature. Energy--information tradeoff induce two discontinuous phase transitions between these three types of optimal LPC networks. We then extend the discussion to detecting and distinguishing between two non-Gaussian input features and observe similar discontinuous phase transitions.

q-bio.NC↗

arXiv2025

The stability of long-range order in disordered systems: A generalized Ding-Zhuang argument

The stability of long-range order against quenched disorder is a central problem in statistical mechanics. This paper develops a generalized framework extending the Ding-Zhuang method and integrated with the Pirogov-Sinai framework, establishing a systematic scheme for studying phase transitions of long-range order in disordered systems. We axiomatize the Ding-Zhuang approach into a theoretical framework consisting of the Peierls condition and a local symmetry condition. For systems in dimensions $d \geq 3$ satisfying these conditions, we prove the persistence of long-range order at low temperatures and under weak disorder, with multiple coexisting distinct Gibbs states. The framework's versatility is demonstrated for diverse models, providing a systematic extension of Peierls methods to disordered systems.

math-ph↗

arXiv2025

Planted vertex cover problem on regular random graphs and nonmonotonic temperature-dependence in the supercooled region

We introduce a planted vertex cover problem on regular random graphs and study it by the cavity method of statistical mechanics. Different from conventional Ising models, the equilibrium ferromagnetic phase transition of this binary-spin two-body interaction system is discontinuous, as the paramagnetic phase is separated from the ferromagnetic phase by an extensive free energy barrier. The free energy landscape can be distinguished into three different types depending on the two degree parameters of the planted graph. The critical inverse temperatures at which the paramagnetic phase becomes locally unstable towards the ferromagnetic phase ($β_{\textrm{pf}}$) and towards spin glass phases ($β_{\textrm{pg}}$) satisfy $β_{\textrm{pf}} > β_{\textrm{pg}}$, $β_{\textrm{pf}} < β_{\textrm{pg}}$ and $β_{\textrm{pf}} = β_{\textrm{pg}}$, respectively, in these three landscapes. A locally stable anti-ferromagnetic phase emerges in the free energy landscape if $β_{\textrm{pf}} < β_{\textrm{pg}}$. When exploring the free energy landscape by stochastic local search dynamics, we find that in agreement with our theoretical prediction, the first-passage time from the paramagnetic phase to the ferromagnetic phase is nonmonotonic with the inverse temperature. The potential relevance of the planted vertex cover model to supercooled glass-forming liquids is briefly discussed.

cond-mat.stat-mech↗

arXiv2024

K-core attack, equilibrium K-core, and kinetically constrained spin system

Kinetically constrained spin systems are toy models of supercooled liquids and amorphous solids. In this Perspective, we revisit the prototypical Fredrickson-Andersen (FA) kinetically constrained model from the viewpoint of K-core combinatorial optimization. Each kinetic cluster of the FA system, containing all the mutually visitable microscopic occupation configurations, is exactly the solution space of a specific instance of the K-core attack problem. The whole set of different jammed occupation patterns of the FA system is the configuration space of an equilibrium K-core problem. Based on recent theoretical results achieved on the K-core attack and equilibrium K-core problems, we discuss the thermodynamic spin glass phase transitions and the maximum occupation density of the fully unfrozen FA kinetic cluster, and the minimum occupation density and extreme vulnerability of the partially frozen (jammed) kinetic clusters. The equivalence between K-core attack and the fully unfrozen FA kinetic cluster also implies a new way of sampling K-core attack solutions.

cond-mat.dis-nn↗

arXiv2024

Energy--Information Trade-off Induces Continuous and Discontinuous Phase Transitions in Lateral Predictive Coding

Lateral predictive coding is a recurrent neural network which creates energy-efficient internal representations by exploiting statistical regularity in sensory inputs. Here we investigate the trade-off between information robustness and energy in a linear model of lateral predictive coding analytically and by numerical minimization of a free energy. We observe several phase transitions in the synaptic weight matrix, especially a continuous transition which breaks reciprocity and permutation symmetry and builds cyclic dominance and a discontinuous transition with the associated sudden emergence of tight balance between excitatory and inhibitory interactions. The optimal network follows an ideal-gas law in an extended temperature range and saturates the efficiency upper-bound of energy utilization. These results bring theoretical insights on the emergence and evolution of complex internal models in predictive processing systems.

q-bio.NC↗

arXiv2023

Hierarchical cycle-tree packing model for $K$-core attack problem

The $K$-core of a graph is the unique maximum subgraph within which each vertex connects to $K$ or more other vertices. The optimal $K$-core attack problem asks to delete the minimum number of vertices from the $K$-core to induce its complete collapse. A hierarchical cycle-tree packing model is introduced here for this challenging combinatorial optimization problem. We convert the temporally long-range correlated $K$-core pruning dynamics into locally tree-like static patterns and analyze this model through the replica-symmetric cavity method of statistical physics. A set of coarse-grained belief propagation equations are derived to predict single vertex marginal probabilities efficiently. The associated hierarchical cycle-tree guided attack ({\tt hCTGA}) algorithm is able to construct nearly optimal attack solutions for regular random graphs and Erdös-Rényi random graphs. Our cycle-tree packing model may also be helpful for constructing optimal initial conditions for other irreversible dynamical processes on sparse random graphs.

cond-mat.dis-nn↗

arXiv2023

Minimum Connected Dominating Set and Backbone of a Random Graph

We study the minimum dominating set problem as a representative combinatorial optimization challenge with a global topological constraint. The requirement that the backbone induced by the vertices of a dominating set should be a connected subgraph makes the problem rather nontrivial to investigate by statistical physics methods. Here we convert this global connectivity constraint into a set of local vertex constraints and build a spin glass model with only five coarse-grained vertex states. We derive a set of coarse-grained belief-propagation equations and obtain theoretical predictions on the relative sizes of minimum dominating sets for regular random and Erdös-Rényi random graph ensembles. We also implement an efficient message-passing algorithm to construct close-to-minimum connected dominating sets and backbone subgraphs for single random graph instances. Our theoretical strategy may also be inspiring for some other global topological constraints.

physics.data-an↗

arXiv2023

Dynamic Gardner crossover in a simple structural glass

The criticality of the jamming transition responsible for amorphous solidification has been theoretically linked to the marginal stability of a thermodynamic Gardner phase. While the critical exponents of jamming appear independent of the preparation history, the pertinence of Gardner physics far from equilibrium is an open question. To fill this gap, we numerically study the nonequilibrium dynamics of hard disks compressed towards the jamming transition using a broad variety of protocols. We show that dynamic signatures of Gardner physics can be disentangled from the aging relaxation dynamics. We thus define a generic dynamic Gardner crossover regardless of the history. Our results show that the jamming transition is always accessed by exploring increasingly complex landscape, resulting in the anomalous microscopic relaxation dynamics that remains to be understood theoretically.

cond-mat.dis-nn↗

arXiv2022

Cycle-tree guided attack of random K-core: Spin glass model and efficient message-passing algorithm

The K-core of a graph is the maximal subgraph within which each vertex is connected to at least K other vertices. It is a fundamental network concept for understanding threshold cascading processes with a discontinuous percolation transition. A minimum attack set contains the smallest number of vertices whose removal induces complete collapse of the K-core. Here we tackle this prototypical optimal initial-condition problem from the spin-glass perspective of cycle-tree maximum packing and propose a cycle-tree guided attack (CTGA) message-passing algorithm. The good performance and time efficiency of CTGA are verified on the regular random and Erdös-Rényi random graph ensembles. Our central idea of transforming a long-range correlated dynamical process to static structural patterns may also be instructive to other hard optimization and control problems.

cond-mat.dis-nn↗

arXiv2022

Lateral predictive coding revisited: Internal model, symmetry breaking, and response time

Predictive coding is a promising theoretical framework in neuroscience for understanding information transmission and perception. It posits that the brain perceives the external world through internal models and updates these models under the guidance of prediction errors. Previous studies on predictive coding emphasized top-down feedback interactions in hierarchical multi-layered networks but largely ignored lateral recurrent interactions. We perform analytical and numerical investigations in this work on the effects of single-layer lateral interactions. We consider a simple predictive response dynamics and run it on the MNIST dataset of hand-written digits. We find that learning will generally break the interaction symmetry between peer neurons, and that high input correlation between two neurons does not necessarily bring strong direct interactions between them. The optimized network responds to familiar input signals much faster than to novel or random inputs, and it significantly reduces the correlations between the output states of pairs of neurons.

q-bio.NC↗

arXiv2021

Circumventing spin glass traps by microcanonical spontaneous symmetry breaking

The planted p-spin interaction model is a paradigm of random-graph systems possessing both a ferromagnetic phase and a disordered phase with the latter splitting into many spin glass states at low temperatures. Conventional simulated annealing dynamics is easily blocked by these low-energy spin glass states. Here we demonstrate that, actually this planted system is exponentially dominated by a microcanonical polarized phase at intermediate energy densities. There is a discontinuous microcanonical spontaneous symmetry breaking transition from the paramagnetic phase to the microcanonical polarized phase. This transition can serve as a mechanism to avoid all the spin glass traps, and it is accelerated by the restart strategy of microcanonical random walk. We also propose an unsupervised learning problem on microcanonically sampled configurations for inferring the planted ground state.

cond-mat.dis-nn↗

arXiv2021

Minimum Long-Loop Feedback Vertex Set and Network Dismantling

Network dismantling aims at breaking a network into disconnected components, and attacking vertices that intersect with many loops has proven to be a most efficient strategy. But the existing loop-focusing methods treat the short loops within densely connected local clusters (e.g., cliques) as equally important as the long loops connecting different clusters. Here we propose for highly clustered artificial and real-world networks a bipartite factor-graph formulation that retains all the long loops while simplifies the local dense clusters as individual factor nodes. We develop a mean-field theory for the associated long-loop feedback vertex set problem and apply its message-passing equation as a solver for network dismantling. The proposed factor-graph loop algorithm outperforms the current state-of-the-art graph loop algorithms by a considerable margin on various real networks. Further improvement in dismantling performance is achievable by optimizing the choice of the local dense clusters.

cs.SI↗

arXiv2021

Vulnerability and Resilience of Social Engagement: Equilibrium Theory

Social networks of engagement sometimes dramatically collapse. A widely adopted paradigm to understand this catastrophe dynamics is the threshold model but previous work only considered the irreversible K-core pruning process and the resulting kinetic activity patterns. Here we study the network alliance problem as a simplified model of social engagement by equilibrium statistical mechanics. Our theory reveals that the surviving kinetic alliances are out-of-equilibrium and atypical configurations which may become highly vulnerable to single-node-triggered cascading failures as they relax towards equilibrium. Our theory predicts that if the fraction of active nodes is beyond a certain critical value, the equilibrium (typical) alliance configurations could be protected from cascading failures by a simple least-effort local intervention strategy. We confirm these results by extensive Monte Carlo simulations.

physics.soc-ph↗

arXiv2020

Maximally flexible solutions of a random $K$-satisfiability formula

Random $K$-satisfiability ($K$-SAT) is a paradigmatic model system for studying phase transitions in constraint satisfaction problems and for developing empirical algorithms. The statistical properties of the random $K$-SAT solution space have been extensively investigated, but most earlier efforts focused on solutions that are typical. Here we consider maximally flexible solutions which satisfy all the constraints only using the minimum number of variables. Such atypical solutions have high internal entropy because they contain a maximum number of null variables which are completely free to choose their states. Each maximally flexible solution indicates a dense region of the solution space. We estimate the maximum fraction of null variables by the replica-symmetric cavity method, and implement message-passing algorithms to construct maximally flexible solutions for single $K$-SAT instances.

cond-mat.dis-nn↗

arXiv2020

Solving Statistical Mechanics on Sparse Graphs with Feedback Set Variational Autoregressive Networks

We propose a method for solving statistical mechanics problems defined on sparse graphs. It extracts a small Feedback Vertex Set (FVS) from the sparse graph, converting the sparse system to a much smaller system with many-body and dense interactions with an effective energy on every configuration of the FVS, then learns a variational distribution parameterized using neural networks to approximate the original Boltzmann distribution. The method is able to estimate free energy, compute observables, and generate unbiased samples via direct sampling without auto-correlation. Extensive experiments show that our approach is more accurate than existing approaches for sparse spin glasses. On random graphs and real-world networks, our approach significantly outperforms the standard methods for sparse systems such as the belief-propagation algorithm; on structured sparse systems such as two-dimensional lattices our approach is significantly faster and more accurate than recently proposed variational autoregressive networks using convolution neural networks.

cond-mat.stat-mech↗