3D Ising Model:The Scaling Equation of State

TL;DR

This paper numerically determines the equation of state for the 3D Ising model's universality class using quantum field theory and renormalization group methods, providing precise amplitude ratios and comparisons with epsilon expansion results.

Contribution

It introduces a novel approach to accurately derive the 3D Ising model's equation of state from perturbative expansions and scaling representations, improving previous estimates.

Findings

Accurate determination of the 3D Ising equation of state

Revised amplitude ratios for the model

Comparison with epsilon expansion results

Abstract

The equation of state of the universality class of the 3D Ising model is determined numerically in the critical domain from quantum field theory and renormalization group techniques. The starting point is the five loop perturbative expansion of the effective potential (or free energy) in the framework of renormalized $\phi^4_3$ field theory. The 3D perturbative expansion is summed, using a Borel transformation and a mapping based on large order behaviour results. It is known that the equation of state has parametric representations which incorporate in a simple way its scaling and regularity properties. We show that such a representation can be used to accurately determine it from the knowledge of the few first coefficients of the expansion for small magnetization. Revised values of amplitude ratios are deduced. Finally we compare the 3D values with the results obtained by the same method from the $\epsilon=4-d$ expansion.