Related papers: The weak limit of Ising models on locally tree-lik…

We study the worst-case mixing time of the global Kawasaki dynamics for the fixed-magnetization Ising model on the class of graphs of maximum degree $\Delta$. Proving a conjecture of Carlson, Davies, Kolla, and Perkins, we show that below…

It has been suggested that an information geometric view of statistical mechanics in which a metric is introduced onto the space of parameters provides an interesting alternative characterisation of the phase structure, particularly in the…

We study the stochastic Ising model on finite graphs with n vertices and bounded degree and analyze the effect of boundary conditions on the mixing time. We show that for all low enough temperatures, the spectral gap of the dynamics with…

We study the critical behavior of the ferromagnetic Ising model on random trees as well as so-called locally tree-like random graphs. We pay special attention to trees and graphs with a power-law offspring or degree distribution whose tail…

We prove the existence of the local weak limit of the measure obtained by sampling random triangulations of size $n$ decorated by an Ising configuration with a weight proportional to the energy of this configuration. To do so, we establish…

Glauber dynamics of the Ising model on a random regular graph is known to mix fast below the tree uniqueness threshold and exponentially slowly above it. We show that Kawasaki dynamics of the canonical ferromagnetic Ising model on a random…

We exhibit an uncountable family of extremal inhomogeneous Gibbs measures of the low temperature Ising model on regular tilings of the hyperbolic plane. These states arise as low temperature perturbations of local ground states having a…

We weaken the assumption of summable variations in a paper by Verbitskiy \cite{verb} to a weaker condition, Berbee's condition, in order for a 1-block factor (a single site renormalisation) of the full shift space on finitely many symbols…

In this note we extend the analysis of a previous paper by the author to the Random Cluster model. The main result being that the pressure of the finite range ferromagnetic Ising model is analytic as a function of the inverse temperature in…

Given n independent Bernoulli(p) random variables X_i, i = 1, ..., n, representing the opinions of individuals connected by an underlying random k-regular graph G_n on {1, ..., n}, we show that when conditioned on an atypical empirical…

We consider the ferromagnetic n.n Ising model on Cayley trees in absence of external fields submitted to a modified majority rule transformation with overlapping cells already known to lead to non-Gibbsian measures. We describe the…

We study the local magnetization in the 2-D Ising model at its critical temperature on a semi-infinite cylinder geometry, and with a nonzero magnetic field $h$ applied at the circular boundary of circumference $\beta$. This model is…

In this paper, we consider the Ising model on random $d$-regular graphs (with $d\ge3$) and Erd\"os-R\'enyi graphs $G(n,d/n)$ (with $d>1$) at the critical temperature. We prove that the \textit{magnetization}, i.e.\ the sum of the spins of a…

We establish tight results for rapid mixing of Gibbs samplers for the Ferromagnetic Ising model on general graphs. We show that if \[(d-1)\tanh\beta<1,\] then there exists a constant C such that the discrete time mixing time of Gibbs…

We solve the growing asymmetric Ising model [Phys. Rev. E 89, 012105 (2014)] in the topologies of deterministic and stochastic (random) scale-free trees predicting its non-monotonous behavior for external fields smaller than the coupling…

We prove Gibbs distribution of two-state spin systems(also known as binary Markov random fields) without hard constrains on a tree exhibits strong spatial mixing(also known as strong correlation decay), under the assumption that, for…

We study the spin n-point functions of the planar Ising model on a simply connected domain \Omega discretised by the square lattice \delta\mathbb{Z}^{2} under near-critical scaling limit. While the scaling limit on the full-plane \mathbb{C}…

Consider the nearest-neighbor Ising model on $\Lambda_n:=[-n,n]^d\cap\mathbb{Z}^d$ at inverse temperature $\beta\geq 0$ with free boundary conditions, and let $Y_n(\sigma):=\sum_{u\in\Lambda_n}\sigma_u$ be its total magnetization. Let $X_n$…

We study a ferromagnetic Ising model on random graphs with a power-law degree distribution and compute the thermodynamic limit of the pressure when the mean degree is finite (degree exponent $\tau>2$), for which the random graph has a…

We prove rigorously that the ferromagnetic Ising model on any nonamenable Cayley graph undergoes a continuous (second-order) phase transition in the sense that there is a unique Gibbs measure at the critical temperature. The proof of this…