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Mean crossover functions for uniaxial three-dimensional Ising-like systems.

Yves Garrabos¹, Claude Bervillier

¹Equipe du Supercritique pour l'Environnement, les Matériaux et l'Espace, Institut de Chimie de la Matière Condensée de Bordeaux, ICMCB-CNRS, UPR 9048, Université Bordeaux I - 87, avenue du Docteur Schweitzer, F 33608 PESSAC Cedex, France.

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|October 10, 2006

Summary

We derived simple expressions for crossover functions in the Phi(d)4(n) model. This provides a criterion to determine if critical or classical behavior dominates, aiding analysis of systems approaching critical points.

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Area of Science:

Statistical Mechanics
Condensed Matter Physics

Background:

The study builds upon previous calculations of critical-to-classical crossover functions within the massive renormalization scheme for the Phi(d)4(n) model.
Focuses on the three-dimensional (d=3), scalar order parameter (n=1) case, relevant to the Ising-like universality class.

Purpose of the Study:

To provide simple expressions for the mean of the maximum and minimum bounds of crossover functions.
To develop a criterion for distinguishing between Ising-like critical and mean-field-like classical crossover behavior.

Main Methods:

Utilized theoretical function properties near the Wilson-Fisher (Ising-like) and Gaussian (mean-field-like) fixed points.
Employed a two-term Wegner expansion valid in preasymptotic domains.
Defined mean crossover functions with three calculated parameters.

Main Results:

Derived explicit expressions for mean crossover functions.
Introduced a parameter-independent criterion to assess the dominance of critical or classical behavior.
Established a method to measure the extent of the Ising-like preasymptotic domain.

Conclusions:

The developed criterion allows for a clear estimation of crossover behavior dominance.
The findings enable coherent analysis of systems with finite asymptotic approaches to critical points.
Offers a controlled number of system-dependent parameters for such analyses, applicable to systems like one-component fluids.