Structure of the broken phase of the sine-Gordon model using functional renormalization

TL;DR

This paper investigates the phase structure of the sine-Gordon model using functional renormalization group methods, revealing fixed points and phase boundaries, and comparing different RG schemes in two and higher dimensions.

Contribution

It introduces a global resolution approach for the effective potential and compares various RG schemes, providing new insights into the fixed points and phase behavior of the sine-Gordon model.

Findings

Phase boundary determined by the Coleman fixed point in 2D.

Existence of IR fixed points in the broken phase independent of bare coupling.

Methodology for using Average action with broken periodicity.

Abstract

We study in this paper the sine-Gordon model using functional Renormalization Group (fRG) at Local Potential Approximation (LPA) using different RG schemes. In $d=2$, using Wegner-Houghton RG we demonstrate that the location of the phase boundary is entirely driven by the relative position to the Coleman fixed point even for strongly coupled bare theories. We show the existence of a set of IR fixed points in the broken phase that are reached independently of the bare coupling. The bad convergence of the Fourier series in the broken phase is discussed and we demonstrate that these fixed-points can be found only using a global resolution of the effective potential. We then introduce the methodology for the use of Average action method where the regulator breaks periodicity and show that it provides the same conclusions for various regulators. The behavior of the model is then discussed in $d\ne 2$ and the absence of the previous fixed points is interpreted.