Related papers: The weak limit of Ising models on locally tree-lik…
Localization properties of the doped Z_2-topological insulator are studied by weak localization theory. The disordered Kane-Mele model for graphene is taken as a prototype, and analyzed with attention to effects of the topological mass…
We introduce a general class of mean-field-like spin systems with random couplings that comprises both the Ising model on inhomogeneous dense random graphs and the randomly diluted Hopfield model. We are interested in quantitative estimates…
We study the identity testing problem in the context of spin systems or undirected graphical models, where it takes the following form: given the parameter specification of the model $M$ and a sampling oracle for the distribution…
We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e.,…
We consider three extensions of the standard 2D Ising model with Glauber dynamics on a finite torus at low temperature. The first model is an anisotropic version, where the interaction energy takes different values on vertical and on…
The study by Glauber of the time-dependent statistics of the Ising chain is extended to the case where each spin is influenced unequally by its nearest neighbours. The asymmetry of the dynamics implies the failure of the detailed balance…
The problem of structure estimation in graphical models with latent variables is considered. We characterize conditions for tractable graph estimation and develop efficient methods with provable guarantees. We consider models where the…
The four dimensional Gaussian random field Ising magnet is investigated numerically at zero temperature, using samples up to size $64^4$, to test scaling theories and to investigate the nature of domain walls and the thermodynamic limit. As…
We analyze Ising/Curie-Weiss models on the (directed) Erd\H{o}s-R\'enyi random graph on $N$ vertices in which every edge is present with probability $p$. These models were introduced by Bovier and Gayrard [J. Stat. Phys., 1993]. We prove a…
We consider a nearest-neighbor SOS model, spin values $0,1,..., m$, $m\geq 2$, on a Cayley tree of order $k$ . We mainly assume that $m=2$ and study translation-invariant (TI) and `splitting' (S) Gibbs measures (GMs). For $m=2$, in the…
A vertex set $S$ is a generalized $k$-independent set if the induced subgraph $G[S]$ contains no tree on $k$ vertices. The generalized $k$-independence number $\alpha_k(G)$ is the maximum size of such a set. For a tree $T$ with $n$…
A matrix is called totally positive (resp. totally nonnegative) if all its minors are positive (resp. nonnegative). Consider the Ising model with free boundary conditions and no external field on a planar graph $G$. Let…
A key insight from statistical physics about spin systems on random graphs is the central role played by Gibbs measures on trees. We determine the local weak limit of the hardcore model on random regular graphs asymptotically until just…
The Ising model in two dimensions with special toroidal boundary conditions is analyzed. These boundary condition, which we call duality twisted boundary conditions, may be interpreted as inserting a specific defect line ("seam") in the…
Inspired by the program of discrete holography, we show that Jackiw-Teitelboim (JT) gravity on a hyperbolic tiling of Euclidean AdS$_2$ gives rise to an Ising model on the dual lattice, subject to a topological constraint. The Ising model…
Let G be an undirected graph on n vertices and let S(G) be the set of all real symmetric n x n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. The inverse inertia problem for G…
We check the existence of a spontaneous magnetisation of Ising and Potts spins on semi-directed Barabasi-Albert networks by Monte Carlo simulations. We verified that the magnetisation for different temperatures $T$ decays after a…
We consider a Glauber dynamics associated with the Ising model on a large two-dimensional box with with minus boundary conditions and in the limit of a vanishing positive external magnetic field. The volume of this box increases…
A dimer mean-field model for the Ising spin-glass is presented. Despite its simplicity it captures some of the essential features of the spin-glass physics. The distribution of the single-spin magnetization is determined from a…
We study the random-cluster model on trees and treelike graphs at low temperatures. This is a model of dependent percolation parametrized by an edge probability $p\in (0,1)$ and a clustering weight $q\in [1,\infty)$, generalizing…