Critical behavior of the Random-Field Ising model at and beyond the Upper Critical Dimension

TL;DR

This study investigates the critical behavior of the Random-Field Ising Model in five to seven dimensions using simulations, confirming mean-field behavior at and above the upper critical dimension with necessary corrections to scaling.

Contribution

It provides numerical evidence for mean-field critical exponents in dimensions d≥6 and emphasizes the importance of corrections to scaling at the upper critical dimension.

Findings

Mean-field exponents observed for d=6,7

Critical exponents: alpha=0, beta=1/2, gamma=1, nu=1/2

Corrections to scaling are essential at and beyond the upper critical dimension

Abstract

The disorder-driven phase transition of the RFIM is observed using exact ground-state computer simulations for hyper cubic lattices in d=5,6,7 dimensions. Finite-size scaling analyses are used to calculate the critical point and the critical exponents of the specific heat, magnetization, susceptibility and of the correlation length. For dimensions d=6,7 which are larger or equal to the assumed upper critical dimension, d_u=6, mean-field behaviour is found, i.e. alpha=0, beta=1/2, gamma=1, nu=1/2. For the analysis of the numerical data, it appears to be necessary to include recently proposed corrections to scaling at and beyond the upper critical dimension.