BKT phase transitions in two-dimensional non-Abelian spin models

TL;DR

This paper argues that two-dimensional non-Abelian U(N) and SU(N) spin models exhibit Berezinskii-Kosterlitz-Thouless (BKT) phase transitions, supported by analytical calculations and numerical simulations, extending the understanding of phase transitions in such models.

Contribution

It demonstrates, through analytical and numerical methods, that non-Abelian U(N) and SU(N) spin models in 2D undergo BKT-like phase transitions, revealing new universality classes.

Findings

U(N) models exhibit BKT-like transitions similar to XY model.

Monte Carlo simulations confirm the universality class of U(2) matches XY.

N>4 SU(N) models show two BKT-type phase transitions.

Abstract

It is argued that two-dimensional U(N) spin models for any N undergo a BKT-like phase transition, similarly to the famous XY model. This conclusion follows from the Berezinskii-like calculation of the two-point correlation function in U(N) models, approximate renormalization group analysis and numerical investigations of the U(2) model. It is shown, via Monte Carlo simulations, that the universality class of the U(2) model coincides with that of the XY model. Moreover, preliminary numerical results point out that two-dimensional SU(N) spin models with the fundamental and adjoint terms and N>4 exhibit two phase transitions of BKT type, similarly to Z(N) vector models.