Triple Point of a Scalar Field Theory on a Fuzzy Sphere

TL;DR

This paper investigates the phase structure of a scalar field theory on a fuzzy sphere, identifying the triple point where three phases meet, and refines its estimated location using the infinite matrix size limit.

Contribution

It locates the triple point of the scalar field theory on a fuzzy sphere with improved accuracy through analysis of the infinite matrix size limit.

Findings

Triple point is closer to the origin than previous estimates.

Location of the triple point is consistent with recent analytic predictions.

Three phases include a non-uniformly ordered phase with no classical counterpart.

Abstract

The model of a scalar field with quartic self-interaction on the fuzzy sphere has three known phases: a uniformly ordered phase, a disordered phase and a non-uniformly ordered phase, the last of which has no classical counterpart. These three phases are expected to meet at a triple point. By studying the infinite matrix size limit, we locate the position of this triple point to within a small triangle in terms of the parameters of the model. We find the triple point is closer to the coordinate origin of the phase diagram than previous estimates but broadly consistent with recent analytic predictions.