Finite size scaling of the correlation length above the upper critical dimension
Disordered Systems and Neural Networks
2009-11-10 v1 Statistical Mechanics
Abstract
We show numerically that correlation length at the critical point in the five-dimensional Ising model varies with system size L as L^{5/4}, rather than proportional to L as in standard finite size scaling (FSS) theory. Our results confirm a hypothesis that FSS expressions in dimension d greater than the upper critical dimension of 4 should have L replaced by L^{d/4} for cubic samples with periodic boundary conditions. We also investigate numerically the logarithmic corrections to FSS in d = 4.
Keywords
Cite
@article{arxiv.cond-mat/0412150,
title = {Finite size scaling of the correlation length above the upper critical dimension},
author = {Jeff L. Jones and A. P. Young},
journal= {arXiv preprint arXiv:cond-mat/0412150},
year = {2009}
}
Comments
5 pages, 6 postscript figures