Noncommutative X-Y model and Kosterlitz Thouless transition

TL;DR

This paper investigates the noncommutative X-Y model through matrix model equivalence to understand the Kosterlitz-Thouless transition, revealing differences in critical coupling values between finite and infinite lattices.

Contribution

It analyzes the noncommutative X-Y model using matrix models to explore phase transition behavior on different lattice sizes, highlighting key differences in critical couplings.

Findings

Critical matrix model coupling is the same for finite and infinite lattices.

Continuum field theory coupling is finite for infinite lattice and zero for finite lattice.

The study clarifies the impact of lattice size on phase transition properties.

Abstract

Matrix models have been shown to be equivalent to noncommutative field theories. In this work we study noncommutative X-Y model and try to understand Kosterlitz Thouless transition in it by analysing the equivalent matrix model. We consider the cases of a finite lattice and infinite lattice separately. We show that the critical value of the matrix model coupling is identical for the finite and infinite lattice cases. However, the critical values of the coupling of the continuum field theory, in the large $ N $ limit, is finite in the infinite lattice case and zero in the case of finite lattice.