Numerical equation of state and other scaling functions from an improved three-dimensional Ising model

TL;DR

This paper uses Monte Carlo simulations to numerically determine universal scaling functions and critical amplitudes of an improved three-dimensional Ising model near its critical point, confirming theoretical predictions.

Contribution

The study provides the first numerical determination of universal scaling functions and amplitudes for the 3D Ising model with external field, validating field theory parametrizations.

Findings

Universal ratios C^+/C^- = 4.756(28), R_{chi} = 1.723(13), Q_c = 0.326(3), Q_2 = 1.201(10)

Excellent agreement with parametric representations of the asymptotic equation of state

Correlation length and susceptibility scaling functions have similar shapes and peak positions

Abstract

We study an improved three-dimensional Ising model with external magnetic field near the critical point by Monte Carlo simulations. From our data we determine numerically the universal scaling functions of the magnetization, that is the equation of state, of the susceptibility and of the correlation length. In order to normalize the scaling functions we calculate the critical amplitudes of the three observables on the critical line, the phase boundary and the critical isochore. These amplitudes lead to the universal ratios C^+/C^-=4.756(28), R_{chi}=1.723(13), Q_c=0.326(3) and Q_2=1.201(10). We find excellent agreement of the data with the parametric representation of the asymptotic equation of state as found by field theory methods. The comparison of the susceptibility data to the corresponding scaling function shows a marginal difference in the symmetric phase, which can be explained by the slightly different value for R_{chi} used in the parametrization. The shape of the correlation-length-scaling function is similar to the one of the susceptibility, as expected from earlier parametrizations. The peak positions of the two scaling functions are coinciding within the error bars.