Accurate Monte Carlo critical exponents for Ising lattices
Abstract
A careful Monte Carlo investigation of the phase transition very close to the critical point (T -> Tc, H -> 0) in relatively large d = 3, s = 1/2 Ising lattices did produce critical exponents beta = 0.3126(4) =~ 5/16, delta^{-1} = 0.1997(4) =~ 1/5 and gamma_{3D} = 1.253(4) =~ 5/4. Our results indicate that, within experimental error, they are given by simple fractions corresponding to the linear interpolations between the respective two-dimensional (Onsager) and four-dimensional (mean field) critical exponents. An analysis of our inverse susceptibility data chi^{-1}(T) vs. /T - Tc/ shows that these data lead to a value of gamma_{3D} compatible with gamma' = gamma and Tc = 4.51152(12), while gamma values obtained recently by high and low temperature series expansions and renormalization group methods are not.
Cite
@article{arxiv.cond-mat/0211270,
title = {Accurate Monte Carlo critical exponents for Ising lattices},
author = {Jorge Garcia and Julio A. Gonzalo and Manuel I. Marques},
journal= {arXiv preprint arXiv:cond-mat/0211270},
year = {2007}
}
Comments
6 pages, 7 figures, submitted to Phys. Rev. B