Two-parameter scaling of correlation functions near continuous phase transitions

TL;DR

This paper introduces a two-parameter scaling form for correlation functions near continuous phase transitions, capturing the crossover from classical to critical behavior and providing a comprehensive description of the critical regime.

Contribution

It proposes a novel two-parameter scaling approach for correlation functions, extending beyond traditional one-parameter scaling, and applies functional renormalization group methods to the Ising universality class.

Findings

The correlation function is described by a two-parameter scaling form.

The classical to critical crossover is captured within this framework.

Approximate calculations for the Ising model are presented.

Abstract

We discuss the order parameter correlation function in the vicinity of continuous phase transitions using a two-parameter scaling form G(k) = k_c^{-2} g(k\xi,k/k_c), where k is the wave-vector, \xi is the correlation length, and the interaction-dependent non-universal momentum scale k_c remains finite at the critical fixed point. The correlation function describes the entire critical regime and captures the classical to critical crossover. One-parameter scaling is recovered only in the limit k/k_c->0. We present an approximate calculation of g(x,y) for the Ising universality class using the functional renormalization group.