Related papers: The restriction of the Ising model to a layer
We study the solid-on-solid interface model above a horizontal wall in three dimensional space, with an attractive interaction when the interface is in contact with the wall, at low temperatures. The system presents a sequence of layering…
The Ising model is studied on a series of hyperbolic two-dimensional lattices which are formed by tessellation of triangles on negatively curved surfaces. In order to treat the hyperbolic lattices, we propose a generalization of the corner…
The aim of this paper is the study of the propagation of a Bessel beam through two absorbing layers, limited by two different half-spaces. Our approach will be based on the scalar analysis, since this analysis was proved to be an excellent…
Following a brief review of the "two-level (tunneling) systems" model of the low-temperature properties of amorphous solids ("glasses"), we ask whether it is in fact the unique explanation of these properties as is usually assumed,…
Although the physical properties of the 2D and 1D Ising models are quite different, we point out an interesting connection between their complex-temperature phase diagrams. We carry out an exact determination of the complex-temperature…
We consider the long-range random field Ising model in dimension $d = 1, 2$, whereas the long-range interaction is of the form $J_{xy} = |x-y|^{-\alpha}$ with $1< \alpha < 3/2$ for $d=1$ and with $2 < \alpha \leq 3$ for $d = 2$. Our main…
We define a 2-dimensional Ising model on a triangulated sphere, $\mathbb S^2$, designed to approach the exact conformal field theory (CFT) in the continuum limit. Surprisingly, the derivation leads to a set of geometric constraints that the…
We consider phase separation on the strip for the two-dimensional Ising model in the near-critical region. Within the framework of field theory, we find exact analytic results for certain two- and three-point correlation functions of the…
We consider the semi-infinite (q)-state Potts model. We prove, for large (q), the existence of a first order surface phase transition between the ordered phase and the the so-called "new low temperature phase" predicted in \cite{Li}, in…
We demonstrate the nontrivial scaling behavior of Ising models defined on (i) a donut-shaped surface and (ii) a curved surface with a constant negative curvature. By performing Monte Carlo simulations, we find that the former model has two…
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…
We study phase separation in two dimensions in the scaling limit below criticality. The general form of the magnetization profile as the volume goes to infinity is determined exactly within the field theoretical framework which explicitly…
Earlier study of quark-hadron phase transition in the Ginzberg-Landau theory is reexamined in the Ising model, so that spatial fluctuations during the transition can be taken into account. Although the dimension of the physical system is 2,…
The high temperature phase of the three dimensional random field Ising model is studied using replica symmetry breaking framework. It is found that, above the ferromagnetic transition temperature T_f, there appears a glassy phase at…
Using the mean field theory, a comparative study of the wetting and layering transitions of a spin-1/2 Ising model with perfect and corrugated surfaces, is established. The phase diagrams are investigated and compared in the presence of…
We consider the three-dimensional Ising model slightly below its critical temperature, with boundary conditions leading to the presence of an interface. We show how the interfacial properties can be deduced starting from the particle modes…
Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sparse graph. In recent years,…
A generalized gauge invariant Ising model on random surfaces with non-trivial topology is proposed and investigated with the dual transformation. It is proved that the model is self-dual in case of a self-dual lattice. In special cases the…
We consider the liquid-vapor type phase transition for fluids confined within spatially periodic external fields. For a fluid in d=3 dimensions, the periodic field induces an additional phase, characterized by large density modulations…
It is shown that quantization of the dynamical systems with second class constraints actually can be reduced to quantization of the systems with first class constraints. The motion of the non-relativistic particle along the plane curve and…