Degeneracy induced scaling of the correlation length for periodic models

TL;DR

This paper investigates how degeneracy in scalar models influences the scaling of correlation length, revealing different types of phase transitions in sine-Gordon models through analysis of their infrared fixed points.

Contribution

It introduces a method to define correlation length in the infrared regime and applies it to classify phase transitions in sine-Gordon models.

Findings

Massive sine-Gordon model shows a continuous phase transition.

Layered sine-Gordon model exhibits an infinite order Kosterlitz-Thouless transition.

Degeneracy induces specific scaling behaviors in correlation length.

Abstract

The broken symmetric phase of scalar models exhibits an infrared fixed point which is induced by the degenerate effective potential. The definition of the correlation length in the infrared regime enables us to determine the type of the phase transition in the model. It is shown that the massive sine-Gordon model exhibits a continuous, while the layered sine-Gordon model has an infinite order Kosterlitz-Thouless type phase transition.