On phase transition in the hard-core model on ${\bf Z}^d$

TL;DR

This paper demonstrates that the hard-core model on the integer lattice ${f Z}^d$ undergoes a phase transition at certain activity levels that decrease to zero as the dimension increases, revealing dimension-dependent behavior.

Contribution

It establishes the existence of a phase transition in the hard-core model on ${f Z}^d$ with a threshold activity function tending to zero as dimension grows.

Findings

Phase transition occurs at activity levels above a function $\lambda(d)$

The threshold activity $\lambda(d)$ tends to zero as $d o fty$

Provides insight into high-dimensional behavior of the hard-core model

Abstract

It is shown that the hard-core model on ${\bf Z}^d$ exhibits a phase transition at activities above some function $\lambda(d)$ which tends to zero as $d\rightarrow \infty$