Accurate Monte Carlo critical exponents for Ising lattices

Jorge Garcı́a and Julio A Gonzalo

Physica A: Statistical Mechanics and its Applications, 2003, vol. 326, issue 3, 464-472

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=12 Ising lattices did produce critical exponents β3D=0.3126(4)≅5/16, δ3D−1=0.1997(4)≅1/5 and γ3D=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 χ−1(T) vs. |T−Tc| shows that these data lead to a value of γ3D compatible with γ′=γ and Tc=4.51152(12), while γ values obtained recently by high and low temperature series expansions and renormalization group methods are not.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:326:y:2003:i:3:p:464-472

DOI: 10.1016/S0378-4371(03)00362-5

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