Comparison of renormalization group schemes for sine-Gordon type models

TL;DR

This paper compares different renormalization group schemes for sine-Gordon models, demonstrating that certain critical parameters are scheme-independent and analyzing phase transition behaviors under quantum fluctuations.

Contribution

It provides a detailed comparison of RG schemes for sine-Gordon models and identifies scheme-independent physical parameters, especially at phase transitions.

Findings

Critical frequency for phase transition is scheme-independent.

Maxwell construction constrains RG flow for the massive sine-Gordon model.

Quantum fluctuations shrink the phase domain with broken periodicity.

Abstract

The scheme-dependence of the renormalization group (RG) flow has been investigated in the local potential approximation for two-dimensional periodic, sine-Gordon type field-theoric models discussing the applicability of various functional RG methods in detail. It was shown that scheme-independent determination of such physical parameters is possible as the critical frequency (temperature) at which Kosterlitz-Thouless-Berezinskii type phase transition takes place in the sine-Gordon and the layered sine-Gordon models, and the critical ratio characterizing the Ising type phase transition of the massive sine-Gordon model. For the latter case the Maxwell construction represents a strong constraint on the RG flow which results in a scheme-independent infrared value for the critical ratio. For the massive sine-Gordon model also the shrinking of the domain of the phase with spontaneously broken periodicity is shown to take place due to the quantum fluctuations.