Renormalization-group flow and asymptotic behaviors at the Berezinskii-Kosterlitz-Thouless transitions

TL;DR

This paper provides a detailed quantitative analysis of the renormalization-group flow at the BKT transition, including critical behaviors and logarithmic corrections, using the sine-Gordon model.

Contribution

It introduces a universal canonical form of the RG beta-functions for the BKT transition, valid to all perturbative orders, and analyzes various critical regimes.

Findings

Derived asymptotic solutions for RG equations in different regimes

Identified universal features of the RG flow at BKT transition

Quantified logarithmic corrections to critical behavior

Abstract

We investigate the general features of the renormalization-group flow at the Berezinskii-Kosterlitz-Thouless (BKT) transition, providing a thorough quantitative description of the asymptotc critical behavior, including the multiplicative and subleading logarithmic corrections. For this purpose, we consider the RG flow of the sine-Gordon model around the renormalizable point which describes the BKT transition. We reduce the corresponding beta-functions to a universal canonical form, valid to all perturbative orders. Then, we determine the asymptotic solutions of the RG equations in various critical regimes: the infinite-volume critical behavior in the disordered phase, the finite-size scaling limit for homogeneous systems of finite size, and the trap-size scaling limit occurring in 2D bosonic particle systems trapped by an external space-dependent potential.