Simulating the scalar field on the fuzzy sphere

TL;DR

This paper numerically investigates the phi^4 scalar field theory on a fuzzy sphere, revealing phase structures and transitions, including uniform, disordered, and non-uniform ordered phases, with analysis of phase coexistence and scaling.

Contribution

It introduces a numerical study of scalar field theory on a fuzzy sphere, highlighting phase behavior and transitions unique to non-commutative geometries.

Findings

Identification of three distinct phases: uniform, disordered, and non-uniform ordered.

Determination of phase coexistence lines and the triple point.

Analysis of phase scaling behaviors.

Abstract

The properties of the phi^4 scalar field theory on a fuzzy sphere are studied numerically. The fuzzy sphere is a discretization of the sphere through matrices in which the symmetries of the space are preserved. This model presents three different phases: uniform and disordered phases, as in the usual commutative scalar field theory, and a non-uniform ordered phase related to UV-IR mixing like non-commutative effects. We have determined the coexistence lines between phases, their triple point and their scaling.