Interplay of fixed points in scalar models

TL;DR

This paper analyzes scalar models with spontaneous symmetry breaking using renormalization group techniques, revealing an infrared fixed point that determines the phase transition characteristics and the correlation length scaling.

Contribution

It demonstrates the existence of an infrared fixed point in the broken phase of scalar models and links it to the phase transition and correlation length behavior.

Findings

Infrared fixed point appears in the broken symmetric phase

Correlation length is associated with a dynamical scale from the fixed point

Critical exponent ν is consistent across crossover and infrared regimes

Abstract

We performed the renormalization group analysis of scalar models exhibiting spontaneous symmetry breaking. It is shown that an infrared fixed point appears in the broken symmetric phase of the models, which induces a dynamical scale, that can be identified with the correlation length. This enables one to identify the type of the phase transition which shows similarity to the one appearing in the crossover scale. The critical exponent $\nu$ of the correlation length also proved to be equal in the crossover and the infrared scaling regimes.