Crossover scaling from classical to non-classical critical behaviour

Abstract

Interacting physical systems in the neighborhood of criticality (and massive continuum field theories) can often be characterized by just two physical scales: a (macroscopic) correlation length and a (microscopic) interaction range, related to the coupling and measured by the Ginzburg number $G$. A critical crossover limit can be defined when both scales become large while their ratio stays finite. The corresponding scaling functions are universal, and they are related to the standard field-theory renormalization-group functions. The critical crossover describes the unique flow from the Gaussian to the nonclassical fixed point.