Critical behavior of the Random-Field Ising model 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.
Keywords
Cite
@article{arxiv.1010.2911,
title = {Critical behavior of the Random-Field Ising model at and beyond the Upper Critical Dimension},
author = {Björn Ahrens and Alexander K. Hartmann},
journal= {arXiv preprint arXiv:1010.2911},
year = {2015}
}
Comments
8 pages and 13 figures; A consise summary of this work can be found in the papercore database at http://www.papercore.org/Ahrens2010