Scaling of the Random-Field Ising Model at Zero Temperature

TL;DR

This paper investigates the critical behavior of the random-field Ising model at zero temperature across different variants and dimensions, revealing universality in 3D and distinct behaviors in 4D, including a possible discontinuous transition.

Contribution

It provides a detailed finite-size scaling analysis of the zero-temperature random-field Ising model, highlighting differences between Gaussian and bimodal variants in 4D.

Findings

Universality class in 3D for three variants

Distinct behavior of Gaussian and bimodal models in 4D

Evidence of a discontinuous magnetization jump in 4D bimodal model

Abstract

The exact determination of ground states of small systems is used in a scaling study of the random-field Ising model. While three variants of the model are found to be in the same universality class in 3 dimensions, the Gaussian and bimodal models behave distinctly in 4 dimensions with the latter apparently having a discontinuous jump in the magnetization. A finite-size scaling analysis is presented for this transition.