The discontinuity of the specific heat for the 5D Ising model

TL;DR

This paper studies the specific heat behavior near the critical point of the 5D Ising model, revealing a discontinuity similar to mean field models, with detailed estimates of critical properties across dimensions 5 to 7.

Contribution

It provides the first detailed estimates of the specific heat discontinuity and critical exponents for the 5D Ising model, extending analysis to 6 and 7 dimensions with improved critical temperature estimates.

Findings

Discontinuity of specific heat at critical point in 5D

Estimated critical exponents for dimensions 5-7

Refined critical temperature estimates aligning with series expansions

Abstract

In this paper we investigate the behaviour of the specific heat around the critical point of the Ising model in dimension 5 to 7. We find a specific heat discontinuity, like that for the mean field Ising model, and provide estimates for the left and right hand limits of the specific heat at the critical point. We also estimate the singular exponents, describing how the specific heat approaches those limits. Additionally, we make a smaller scale investigation of the same properties in dimension 6 and 7, and provide strongly improved estimates for the critical termperature $K_c$ in $d=5,6,7$ which bring the best MC-estimate closer to those obtained by long high temperature series expanions.