Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems

TL;DR

This paper computes high-temperature series for a 3D Ising model with improved potentials, accurately estimates critical exponents, and constructs a parametric equation of state using a new approximation scheme.

Contribution

It introduces a systematic approximation scheme for the critical equation of state and provides high-precision estimates of critical exponents for 3D Ising-like systems.

Findings

Critical exponents estimated with high accuracy.

Constructed parametric representations of the critical equation of state.

Determined universal amplitude ratios and compared with other results.

Abstract

High-temperature series are computed for a generalized $3d$ Ising model with arbitrary potential. Two specific ``improved'' potentials (suppressing leading scaling corrections) are selected by Monte Carlo computation. Critical exponents are extracted from high-temperature series specialized to improved potentials, achieving high accuracy; our best estimates are: $\gamma=1.2371(4)$, $\nu=0.63002(23)$, $\alpha=0.1099(7)$, $\eta=0.0364(4)$, $\beta=0.32648(18)$. By the same technique, the coefficients of the small-field expansion for the effective potential (Helmholtz free energy) are computed. These results are applied to the construction of parametric representations of the critical equation of state. A systematic approximation scheme, based on a global stationarity condition, is introduced (the lowest-order approximation reproduces the linear parametric model). This scheme is used for an accurate determination of universal ratios of amplitudes. A comparison with other theoretical and experimental determinations of universal quantities is presented.