Renormalization-Group Analysis of the Generalized sine-Gordon Model and of the Coulomb Gas for d >= 3 Dimensions

TL;DR

This paper derives and compares renormalization-group flow equations for the generalized sine-Gordon model and Coulomb gas in dimensions d >= 3, revealing UV scaling laws and IR behavior, with implications for phase structure and scheme dependence.

Contribution

It provides a comprehensive RG analysis of GSGM and Coulomb gas in higher dimensions, including numerical verification of IR fixed points and scheme dependence insights.

Findings

UV scaling laws are dimension-independent for d >= 3

Blocked potential tends to a constant in 4D GSGM

RG flow depends on the renormalization scheme used

Abstract

Renormalization-group (RG) flow equations have been derived for the generalized sine-Gordon model (GSGM) and the Coulomb gas (CG) in d >= 3 of dimensions by means of Wegner's and Houghton's, and by way of the real-space RG approaches. The UV scaling laws determined by the leading-order terms of the flow equations are in qualitative agreement for all dimensions d >= 3, independent of the dimensionality, and in sharp contrast to the special case d = 2. For the 4-dimensional GSGM it is demonstrated explicitly (by numerical calculations), that the blocked potential tends to a constant effective potential in the infrared (IR) limit, satisfying the requirements of periodicity and convexity. The comparison of the RG flows for the three-dimensional GSGM, the CG, and the vortex-loop gas reveals a significant dependence on the renormalization schemes and the approximations used.