Related papers: The torus plateau for the high-dimensional Ising m…
We investigate the scaling of the largest critical percolation cluster on a large d-dimensional torus, for nearest-neighbor percolation in high dimensions, or when d>6 for sufficient spread-out percolation. We use a relatively simple…
We show that the six-vertex model with parameter $c\in[\sqrt 3, 2]$ on a square lattice torus has an ergodic infinite-volume limit as the size of the torus grows to infinity. Moreover we prove that for $c\in[\sqrt{2+\sqrt 2}, 2]$, the…
We study microscopic observables of the Discrete Gaussian model (i.e., the Gaussian free field restricted to take integer values) at high temperature using the renormalisation group method. In particular, we show the central limit theorem…
The random-field Ising model shows extreme critical slowdown that has been described by activated dynamic scaling: the characteristic time for the relaxation to equilibrium diverges exponentially with the correlation length, $\ln \tau\sim…
For the Ising model defined on $a\mathbb{Z}^2$ at critical temperature with external field $a^{15/8}h$, we give a simple and elementary proof that its truncated two-point function decays exponentially. The proof combines the high…
In 2002 Biskup et al. [Europhys. Lett. 60, 21 (2002)] sketched a rigorous proof for the behavior of the 2D Ising lattice gas, at a finite volume and a fixed excess \delta M of particles (spins) above the ambient gas density (spontaneous…
Two dimensional quantum gravity coupled to a conformally invariant matter field of central charge c=n/2, is represented, in a discretized version, by n independent Ising spins per cell of the triangulations of a random surface. The matrix…
We reconsider Ising spins in a Gaussian random field within the replica formalism. The corresponding continuum model involves several coupling constants beyond the single one which was considered in the standard $\phi^4$ theory approach.…
We consider a RG flow in certain 2D coset models perturbed by the least relevant field. In the case of the symmetric su(2) coset model we show, up to second order of the perturbation theory, that there exists a nontrivial IR fixed point.We…
The majority-voter model is studied by Monte Carlo simulations on hypercubic lattices of dimension $d=2$ to 7 with periodic boundary conditions. The critical exponents associated to the Finite-Size Scaling of the magnetic susceptibility are…
We consider the critical FK-Ising measure $\phi_{\beta_c}$ on $\mathbb Z^d$ with $d\geq 3$. We construct the measure $\phi^\infty:=\lim_{|x|\rightarrow \infty}\phi_{\beta_c}[\:\cdot\: |\: 0\leftrightarrow x]$ and prove it satisfies…
We perform Monte Carlo simulations of a three-dimensional spin system with a Hamiltonian which contains only four-spin interaction term. This system describes random surfaces with extrinsic curvature - gonihedric action. We study the…
We performed a high statistics simulation of Ising spins coupled to 2D quantum gravity on toroidal geometries. The tori were triangulated using the Regge calculus approach and contained up to $512^2$ vertices. We used a constant area…
We consider the zero-temperature fixed points controlling the critical behavior of the $d$-dimensional random-field Ising, and more generally $O(N)$, models. We clarify the nature of these fixed points and their stability in the region of…
We perform a high-statistics simulation of the three-dimensional randomly dilute Ising model on cubic lattices $L^3$ with $L\le 256$. We choose a particular value of the density, x=0.8, for which the leading scaling corrections are…
We investigate the geometry of a typical spin cluster in random triangulations sampled with a probability proportional to the energy of an Ising configuration on their vertices, both in the finite and infinite volume settings. This model is…
The Ising-Kac model is a variant of the ferromagnetic Ising model in which each spin variable interacts with all spins in a neighbourhood of radius $\gamma^{-1}$ for $\gamma \ll 1$ around its base point. We study the Glauber dynamics for…
The Discrete Gaussian model is the lattice Gaussian free field conditioned to be integer-valued. In two dimensions, at sufficiently high temperature, we show that the scaling limit of the infinite-volume gradient Gibbs state with zero mean…
Following numerous earlier studies, extensive simulations and analyses were made on the continuous interaction distribution Gaussian model and the discrete bimodal interaction distribution Ising Spin Glass (ISG) models in dimension two…
In this paper, we investigate the dynamics of the two-dimensional Ising model with stochastic resetting, utilizing a constant resetting rate procedure with zero-strength initial magnetization. Our results reveal the presence of a…