Revising the universality class of the four-dimensional Ising model

TL;DR

This study uses large-scale simulations to analyze the specific heat behavior of the 4D Ising model at criticality, revealing it has a bounded specific heat and thus belongs to a different universality class than the $$-model, which diverges logarithmically.

Contribution

It provides the largest simulation data set for the 4D Ising model, clarifying its universality class distinction from the $$-model in four dimensions.

Findings

Ising model has bounded specific heat at criticality

$$-model exhibits logarithmic divergence

Models belong to different universality classes in 4D

Abstract

The aim of this paper is to determine the behavior of the specific heat of the 4-dimensional Ising model at the critical temperature, and via that determine if the Ising model and the $\phi^4$-model belong to the same universality class in dimension 4. In order to do this we have carried out what is currently the largest scale simulations of the 4-dimensional Ising model, extending the lattices size up to $L=256$ and the number of samples per size by several orders of magnitude compared to earlier works, keeping track of data for both the canonical and microcanonical ensembles. Our conclusion is that the Ising model has a bounded specific heat, while the $\phi^4$-model is known to have a logarithmic divergence at the critical point. Hence the two models belong to distinct universality classes in dimension 4.