Accurate Monte Carlo critical exponents for Ising lattices

TL;DR

This paper presents precise Monte Carlo calculations of critical exponents for the 3D Ising model, showing they approximate simple fractions between 2D and 4D values, with implications for understanding phase transitions.

Contribution

The study provides highly accurate Monte Carlo estimates of critical exponents for the 3D Ising lattice, revealing they align with simple fractional values interpolated between 2D and 4D cases.

Findings

Critical exponents approximate simple fractions (~5/16, ~1/5, ~5/4).

Critical temperature Tc determined as 4.51152(12).

Results support fractional interpolation between 2D and 4D exponents.

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.