Related papers: Continuity of the Ising phase transition on noname…

The purpose of this modest note is to point out that the proof of the recent result of Huchcroft concerning continuity of phase transition in Bernoulli percolation is applicable to the setting of the Ising model with free boundary…

We prove that at any inverse temperature $\beta$ and on any transitive amenable graph, the automorphism-invariant Gibbs states of the ferromagnetic Ising model are convex combinations of the plus and minus states. This is obtained for a…

Ising model without external field on an infinite Lorentzian triangulation sampled from the uniform distribution is considered. We prove uniqueness of the Gibbs measure in the high temperature region and coexistence of at least two Gibbs…

We prove that all the translation invariant Gibbs states of the Ising model are a linear combination of the pure phases $\mu^+,\mu^-$ in the phase transition regime. This implies that the average magnetization is continuous in the phase…

We present a sufficient condition for the presence of spontaneous magnetization for the Ising model on a general graph, related to its long-range topology. Applying this condition we are able to prove the existence of a phase transition at…

We provide a new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model. The proof applies to infinite range models on arbitrary locally finite transitive infinite graphs. For Bernoulli percolation, we…

In this paper we prove the existence of phase transitions at finite temperature for O(n) classical ferromagnetic spin models on infrared finite graphs. Infrared finite graphs are infinite graphs with $\lim {m\to 0^+} {\bar Tr (L+m)^{-1} <…

We show that the nearest neighbors Ising model on the Cayley tree exhibits new temperature driven phase transitions. These transitions holds at various inverse temperatures different from the critical one. They are depicted by a change in…

The Dyson-Ising ferromagnet is a one-dimensional Ising model with a power law interaction. When the power is between -1 and -2, the model has a phase transition. Van Enter and Le Ny proved that at sufficiently low temperatures the…

We examine Ising models with heat-bath dynamics on directed networks. Our simulations show that Ising models on directed triangular and simple cubic lattices undergo a phase transition that most likely belongs to the Ising universality…

A periodic Ising model is one endowed with interactions that are invariant under translations of members of a full-rank sublattice $\mathfrak{L}$ of $\mathbb{Z}^2$. We give an exact, quantitative description of the critical temperature,…

We study phase transitions in the Ising model on random graphs using graph limits. We show that the critical temperatures are determined by the eigenvalues of the kernel operator associated with the graph limit. Bifurcation diagrams for…

The spontaneous magnetization is proved to vanish continuously at the critical temperature for a class of ferromagnetic Ising spin systems which includes the nearest neighbor ferromagnetic Ising spin model on $\mathbb Z^d$ in $d=3$…

We consider the Ising model on the two-dimensional square lattice where on each horizontal line, called "layer", the interaction is given by a ferromagnetic Kac potential with coupling strength $J_\gamma(x,y)=\gamma J(\gamma(x-y))$, where…

We study the metastability of the ferromagnetic Ising model on a random $r$-regular graph in the zero temperature limit. We prove that in the presence of a small positive external field the time that it takes to go from the all minus state…

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…

The finite size analysis of the nonequilibrium phase transition, in two dimensional Ising ferromagnet driven by plane propagating magneticwave, is studied by Monte Carlo simulation. It is observed that the system undergoes a nonequilibrium…

Magnetic phenomena of the superantiferromagnetic Ising model in both uniform longitudinal ($H$) and transverse ($\Omega $) magnetic fields are studied by employing a mean-field variational approach based on Peierls-Bogoliubov inequality for…

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…

Let $G$ be the product of finitely many trees $T_1\times T_2 \times \cdots \times T_N$, each of which is regular with degree at least three. We consider Bernoulli bond percolation and the Ising model on this graph, giving a short proof that…