Classical-to-critical crossovers from field theory

TL;DR

This paper provides accurate classical-to-critical crossover expressions in 3D field theory for various thermodynamic quantities in n-vector and Ising models, incorporating high-order loop calculations and current critical parameter estimates.

Contribution

It extends previous work by including seventh-loop order calculations and current universal critical quantities to refine crossover descriptions in 3D models.

Findings

Accurate crossover functions for correlation length, susceptibility, and specific heat.

Enhanced theoretical understanding of classical-to-critical transition in 3D models.

Inclusion of high-order loop calculations improves precision of critical behavior predictions.

Abstract

We extent the previous determinations of nonasymptotic critical behavior of Phys. Rev B32, 7209 (1985) and B35, 3585 (1987) to accurate expressions of the complete classical-to-critical crossover (in the 3-d field theory) in terms of the temperature-like scaling field (i.e., along the critical isochore) for : 1) the correlation length, the susceptibility and the specific heat in the homogeneous phase for the n-vector model (n=1 to 3) and 2) for the spontaneous magnetization (coexistence curve), the susceptibility and the specific heat in the inhomogeneous phase for the Ising model (n=1). The present calculations include the seventh loop order of Murray and Nickel (1991) and closely account for the up-to-date estimates of universal asymptotic critical quantities (exponents and amplitude combinations) provided by Guida and Zinn-Justin [J. Phys. A31, 8103 (1998)].