An improved upper bound for critical value of the contact process on $\mathbb{Z}^d$ with $d\geq 3$

TL;DR

This paper improves the upper bound for the critical infection rate in the contact process on high-dimensional integer lattices, providing a tighter estimate specifically for three dimensions.

Contribution

It establishes a new, lower upper bound for the critical value of the contact process on  lattices with d, refining previous estimates.

Findings

 critical value    0.384 for d=3

Improved upper bounds for  contact process critical value

Enhanced understanding of phase transition thresholds in high-dimensional lattices

Abstract

In this paper we give an improved upper bound for critical value $\lambda_c$ of the basic contact process on the lattice $\mathbb{Z}^d$ with $d\geq 3$. As a direct corollary of out result, \[ \lambda_c\leq 0.384. \] when $d=3$.