Analytic application of the mean crossover function to the description of the isothermal compressibility of xenon

TL;DR

This paper applies mean crossover functions derived from renormalization group theory to model the isothermal compressibility of xenon near its critical point, analyzing the validity range and Ising behavior in the preasymptotic domain.

Contribution

It introduces a novel application of mean crossover functions from the Massive Renormalization scheme to describe xenon's critical compressibility behavior.

Findings

The crossover functions accurately represent xenon's compressibility near criticality.

The validity range of the model is established and discussed.

The Ising nature of the crossover description is confirmed in the preasymptotic domain.

Abstract

We use the mean crossover functions [Garrabos and Bervillier, Phys Rev. E 74, 021113 (2006)] estimated from the bounded results of the Massive Renormalization scheme applied to the $\Phi_{d}^{4}(n)$ model in three dimensions ($d=3$) and scalar order parameter ($n=1$) [Bagnuls and Bervillier, Phys. Rev. E 65, 066132 (2002)], to represent the singular behavior of the isothermal compressibility of xenon along the critical isochore in the homogeneous preasymptotic domain. The validity range and the Ising nature of the crossover description are discussed in terms of a single scale factor whose value can be analytically estimated beyond the Ising-like preasymptotic domain.