High Precision Verification of the Kosterlitz Thouless Scenario

TL;DR

This paper rigorously verifies the Kosterlitz Thouless scenario in three SOS models by matching their RG flows with an exactly solvable model, providing high-precision estimates of critical parameters.

Contribution

It introduces a method for high-precision verification of the KT scenario by RG flow matching with an exactly solvable model, applicable to various SOS models.

Findings

Confirmed the KT scenario for three SOS models.

Provided high-precision estimates of critical couplings.

Demonstrated the effectiveness of RG flow matching.

Abstract

We verify the Kosterlitz Thouless scenario for three different SOS (solid-on-solid) models, including the dual transforms of XY-models with Villain and with cosine action. The method is based on a matching of the renormalization group (RG) flow of the candidate models with the flow of a bona fide KT model, the exactly solvable BCSOS model. We obtain high precision estimates for the critical couplings and other non-universal quantities.