A numerical approach to harmonic non-commutative spectral field theory

TL;DR

This paper numerically investigates a non-commutative gauge theory on Moyal space using matrix approximations and Monte Carlo simulations, revealing potential phase transitions and highlighting differences from the original spectral model.

Contribution

It introduces a numerical method for analyzing non-commutative spectral field theories via matrix approximations and Monte Carlo techniques.

Findings

Peak in specific heat suggests possible phase transition.

Finite matrix models differ from the spectral model in the infinite limit.

Numerical results provide insights into non-commutative gauge theories.

Abstract

We present a first numerical investigation of a non-commutative gauge theory defined via the spectral action for Moyal space with harmonic propagation. This action is approximated by finite matrices. Using Monte Carlo simulation we study various quantities such as the energy density, the specific heat density and some order parameters, varying the matrix size and the independent parameters of the model. We find a peak structure in the specific heat which might indicate possible phase transitions. However, there are mathematical arguments which show that the limit of infinite matrices is very different from the original spectral model.