Crossover scaling from classical to nonclassical critical behavior

TL;DR

This paper investigates the universal crossover from classical to nonclassical critical behavior, analyzing how the Ginzburg number governs the transition and exploring the associated scaling functions through theoretical models.

Contribution

It introduces a universal description of the critical crossover using scaling functions related to renormalization-group theory, demonstrated explicitly in the large-N limit of the O(N) model.

Findings

Scaling functions are universal across microscopic mechanisms.

Explicit demonstration in the large-N limit of the O(N) model.

Nonmonotonic behavior of susceptibility exponent in 3D Ising model.

Abstract

We study the crossover between classical and nonclassical critical behaviors. The critical crossover limit is driven by the Ginzburg number G. The corresponding scaling functions are universal with respect to any possible microscopic mechanism which can vary G, such as changing the range or the strength of the interactions. The critical crossover describes the unique flow from the unstable Gaussian to the stable nonclassical fixed point. The scaling functions are related to the continuum renormalization-group functions. We show these features explicitly in the large-N limit of the O(N) phi^4 model. We also show that the effective susceptibility exponent is nonmonotonic in the low-temperature phase of the three-dimensional Ising model.