The \phi_3^4 lattice field theory viewed from the high-temperature side

TL;DR

This paper uses extended high-temperature series expansions to analyze the critical behavior of the three-dimensional ^4 lattice scalar field theory, confirming universality and accurately determining critical parameters.

Contribution

It provides high-precision estimates of critical exponents and coupling constants using series expansions, and identifies conditions for minimal corrections to scaling.

Findings

Critical exponents b3=1.2373(2), bd=0.6301(2)

Universal critical parameters confirmed for both lattices

Identification of self-coupling value minimizing corrections

Abstract

We analyze high-temperature series expansions of the two-point and four-point correlation-functions in the three-dimensional euclidean lattice scalar field theory with quartic self-coupling, which have been recently extended through twenty-fifth order for the simple-cubic and body-centered-cubic lattices. We conclude that the length of the present series is sufficient for a fairly accurate description of the critical behavior of the model and confirm the validity of universality, scaling and hyperscaling. In the case of the body-centered-cubic lattice, we determine the value of the quartic self-coupling for which the leading corrections to scaling approximately vanish and correspondingly the universal critical parameters can be determined with high accuracy. In particular, for the susceptibility and the correlation-length exponents we find \gamma=1.2373(2) and \nu=0.6301(2). For the four-point renormalized coupling we find g=23.56(3). In the case of the simple-cubic lattice our results are consistent with earlier estimates.