相关论文: A Spectral Condition for Spectral Gap: Fast Mixing…

We consider generalized quantum Ising models, including those which could describe disordered materials or quantum annealers, and we prove that for all temperatures above a system-size independent threshold the path integral Monte Carlo…

A two-temperature Ising-Schelling model is introduced and studied for describing human segregation. The self-organized Ising model with Glauber kinetics simulated by M\"uller et al. exhibits a phase transition between segregated and mixed…

Two kinds of recursive lattices with the same coordination number but different unit cells (2-D square and 3-D cube) are constructed and the antiferromagnetic Ising model is solved exactly on them to study the stable and metastable states.…

We extend recent higher order concentration results in the discrete setting to include functions of possibly dependent variables whose distribution (on the product space) satisfies a logarithmic Sobolev inequality with respect to a…

Much recent rigorous study of the classical ferromagnetic Ising model has been powered by its graphical representations, such as the random current and loop O(1) model (high temperature expansion). In this paper, we prove uniqueness of…

We use a Harnack-type inequality on exit times and spectral bounds to characterize upper bounds of the heat kernel associated with any regular Dirichlet form without killing part, where the scale function may vary with position. We further…

We show that the equilibrium interfaces in the disordered phase have critical percolation fractal dimension over a wide range of length scales. We confirm that the system falls out of equilibrium at a temperature that depends on the cooling…

This paper proves the strong parabolic Harnack inequality for local weak solutions to the heat equation associated with time-dependent (nonsymmetric) bilinear forms. The underlying metric measure Dirichlet space is assumed to satisfy the…

We consider Markov random fields of discrete spins on the lattice $\Zd$. We use a technique of coupling of conditional distributions. If under the coupling the disagreement cluster is "sufficiently" subcritical, then we prove the Poincar\'e…

We prove that the spectral gap of the Swendsen-Wang process for the Potts model on graphs with bounded degree is bounded from below by some constant times the spectral gap of any single-spin dynamics. This implies rapid mixing of the…

Consider Glauber dynamics for the Ising model on the hypercubic lattice with a positive magnetic field. Starting from the minus configuration, the system initially settles into a metastable state with negative magnetization. Slowly the…

We establish upper bounds for the spectral gap of the stochastic Ising model at low temperature in an N-by-N box, with boundary conditions which are ``plus'' except for small regions at the corners which are either free or ``minus.'' The…

We study a large class of critical two-dimensional Ising models namely critical Z-invariant Ising models on periodic graphs, example of which are the classical square, triangular and honeycomb lattice at the critical temperature. Fisher…

Phase separation is a fairly common physical phenomenon with examples including the formation of water droplets from humid air (fog, rain), the separation of a crystalline structure from an isotropic material such as a liquid or even the…

The Ising model exhibits qualitatively different properties in hyperbolic space in comparison to its flat space counterpart. Due to the negative curvature, a finite fraction of the total number of spins reside at the boundary of a volume in…

Kinetic Ising models on the square lattice with both nearest-neighbor interactions and self-interaction are studied for the cases of random sequential updating and parallel updating. The equilibrium phase diagrams and critical dynamics are…

We present examples of isospectral operators that do not have the same heat content. Several of these examples are planar polygons that are isospectral for the Laplace operator with Dirichlet boundary conditions. These include examples with…

Among the Renormalization Group Theory scaling rules relating critical exponents, there are hyperscaling rules involving the dimension of the system. It is well known that in Ising models hyperscaling breaks down above the upper critical…

Notwithstanding great strides that statistical mechanics has made in recent decades, an analytic solution of arguably the simplest model of relaxation dynamics, the Ising model in an applied external field remains elusive even in $1d$.…

In the ordered phase of the 3D Ising model, minority spin clusters are surrounded by a boundary of dual plaquettes. As the temperature is raised, these spin clusters become more numerous, and it is found that eventually their boundaries…