Related papers: The restriction of the Ising model to a layer
We consider the three-dimensional Ising model in a half-space with a boundary field (no bulk field). We compute the low-temperature expansion of layering transition lines.
The geometrical approach to phase transitions is illustrated by simulating the high-temperature representation of the Ising model on a square lattice.
The coverage of vicinal, stepped surfaces with molecules is simulated with the help of a two-dimensional Ising model including local distortions and an Ehrlich-Schwoebel barrier term at the steps. An effective two-spin model is capable to…
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…
A model in statistical mechanics, characterised by the corresponding Gibbs measure, is a subset of the totality of probability distributions on the phase space. The shape of this subset, i.e., the geometry, then plays an important role in…
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…
We discuss the interrelation between phase transitions in interacting lattice or continuum models, and the existence of infinite clusters in suitable random-graph models. In particular, we describe a random-geometric approach to the phase…
Properties of the two dimensional Ising model with fixed magnetization are deduced from known exact results on the two dimensional Ising model. The existence of a continuous phase transition is shown for arbitrary values of the fixed…
In this paper, we survey and discuss various surface phenomena such as prewetting, layering and faceting for a family of two- and three-dimensional low-temperature models of statistical mechanics, notably Ising models and (2+1)-dimensional…
We contribute to the mathematical theory of the design of low temperature Ising machines, a type of experimental probabilistic computing device implementing the Ising model. Encoding the output of a function in the ground state of a…
The infinite-volume limit behavior of the 2d Ising model under possibly strong random boundary conditions is studied. The model exhibits chaotic size-dependence at low temperatures and we prove that the `+' and `-' phases are the only…
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…
Using Monte Carlo simulations we study the two-dimensional Ising model on triangular, square, and hexagonal lattices with various topologies. We focus on the behavior of the magnetic susceptibility and of the specific heat near the critical…
The scaling limit of the two-dimensional Ising model in the plane of temperature and magnetic field defines a field theory which provides the simplest illustration of non-trivial phenomena such as spontaneous symmetry breaking and…
The nature of the Abelian Higgs Model phase transition is investigated. A variational approximation is used in the evaluation of the relevant finite temperature effective potential. Some of the results presented are valid not only in the…
We report new results on complex-temperature properties of Ising models. These include studies of the $s=1/2$ model on triangular, honeycomb, kagom\'e, $3 \cdot 12^2$, and $4 \cdot 8^2$ lattices. We elucidate the complex--$T$ phase diagrams…
By applying a recently proposed mapping, we derive exactly the upper phase boundary of several Ising spin glass models defined over static graphs and random graphs, generalizing some known results and providing new ones.
The global phase diagram of wetting in the two-dimensional (2d) Ising model is obtained through exact calculation of the surface excess free energy. Besides a surface field for inducing wetting, a surface-coupling enhancement is included.…
We construct a parallel stochastic dynamics with invariant measure converging to the Gibbs measure of the low temperature Ising model. The proof of such convergence requires a polymer expansion based on suitably defined Peierls-type…
The effect of edge on wetting and layering transitions of a three-dimensional spin-1/2 Ising model is investigated, in the presence of longitudinal and surface magnetic fields, using mean field (MF) theory and Monte Carlo (MC) simulations.…