Related papers: Random cluster models on random graphs
We present a new method to close the Master Equation representing the continuous time dynamics of Ising interacting spins. The method makes use of the the theory of Random Point Processes to derive a master equation for local conditional…
The Ising model on networks plays a fundamental role as a testing ground for understanding cooperative phenomena in complex systems. Here we solve the synchronous dynamics of the Ising model on random graphs with an arbitrary degree…
Spin systems are fundamental models of statistical physics that provide insight into collective behavior across scientific domains. Their interest to computer science stems in part from the deep connection between the phase transitions they…
The polymer model framework is a classical tool from statistical mechanics that has recently been used to obtain approximation algorithms for spin systems on classes of bounded-degree graphs; examples include the ferromagnetic Potts model…
The aim of this paper is to prove central limit theorems with respect to the annealed measure for the magnetization rescaled by $\sqrt{N}$ of Ising models on random graphs. More precisely, we consider the general rank-1 inhomogeneous random…
We analyze the behavior of the ensemble of surface boundaries of the critical clusters at $T=T_c$ in the $3d$ Ising model. We find that $N_g(A)$, the number of surfaces of given genus $g$ and fixed area $A$, behaves as $A^{-x(g)}$ $e^{-\mu…
The vertices of the Cayley graph of a finitely generated semigroup form a set of sites which can be labeled by elements of a finite alphabet in a manner governed by a nonnegative real interaction matrix, respecting nearest neighbor…
We prove a hardness of sampling result for the anti-ferromagnetic Ising model on random graphs of average degree $d$ for large constant $d$, proving that when the normalized inverse temperature satisfies $\beta>1$ (asymptotically…
The theoretical phase diagrams of the magnetic (Ising) lattice fluid in an external magnetic field is presented. It is shown that, depending on the strength of the nonmagnetic interaction between particles, various effects of external field…
The replicated field theory of the random field Ising model involves the couplings of replicas of different indices. The resulting correlation functions involve a superposition of different types of long distance behaviours. However the…
We write down matrix models for Ising spins with zero external field on the vertices of dynamical triangulated random surfaces (DTRS) and dynamically quadrangulated random surfaces (DQRS) and compare these with the standard matrix model…
We examine the geometrical and topological properties of surfaces surrounding clusters in the 3--$d$ Ising model. For geometrical clusters at the percolation temperature and Fortuin--Kasteleyn clusters at $T_c$, the number of surfaces of…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
We develop a transfer matrix method to compute exactly the spin-spin correlation functions of Bethe lattice spin models in the external magnetic field h and for any temperature T. We first compute the correlation function for the most…
We construct the exact partition function of the Potts model on a complete graph subject to external fields with linear and nematic type couplings. The partition function is obtained as a solution to a linear diffusion equation and the free…
Spin systems exposed to the influence of random magnetic fields are paradigmatic examples for studying the effect of quenched disorder on condensed-matter systems. In this context, previous studies have almost exclusively focused on systems…
The large amounts of data from molecular biology and neuroscience have lead to a renewed interest in the inverse Ising problem: how to reconstruct parameters of the Ising model (couplings between spins and external fields) from a number of…
We consider homogeneous factor models on uniformly sparse graph sequences converging locally to a (unimodular) random tree $T$, and study the existence of the free energy density $\phi$, the limit of the log-partition function divided by…
Spectral clustering is popular among practitioners and theoreticians alike. While performance guarantees for spectral clustering are well understood, recent studies have focused on enforcing ``fairness'' in clusters, requiring them to be…
Spin models on quenched random graphs are related to many important optimization problems. We give a new derivation of their mean-field equations that elucidates the role of the natural order parameter in these models.