Universal Amplitude Ratios in the Ising Model in Three Dimensions

TL;DR

This paper uses high-precision Monte Carlo simulations to accurately determine the universal amplitude ratio and critical exponents of the three-dimensional Ising model, providing results that support some previous estimates and challenge recent conjectures.

Contribution

The study provides precise numerical estimates of the universal amplitude ratio and critical exponents in the 3D Ising model using advanced Monte Carlo methods.

Findings

Amplitude ratio A+/A- = 0.56(3)

Correlation-length exponent bda0= 0.63048(32)

Specific-heat exponent ba0= 0.1086(10)

Abstract

We use a high-precision Monte Carlo simulation to determine the universal specific-heat amplitude ratio A+/A- in the three-dimensional Ising model via the impact angle \phi of complex temperature zeros. We also measure the correlation-length critical exponent \nu from finite-size scaling, and the specific-heat exponent \alpha through hyperscaling. Extrapolations to the thermodynamic limit yield \phi = 59.2(1.0) degrees, A+/A- = 0.56(3), \nu = 0.63048(32) and \alpha = 0.1086(10). These results are compatible with some previous estimates from a variety of sources and rule out recently conjectured exact values.