First numerical approach to a Grosse-Wulkenhaar model

TL;DR

This paper presents the first numerical study of a Grosse-Wulkenhaar non-commutative field theory using spectral triples and Monte Carlo simulations, exploring phase transitions and physical quantities.

Contribution

It introduces a novel numerical approach to analyze a Grosse-Wulkenhaar model based on spectral action and non-commutative geometry techniques.

Findings

Energy density and specific heat density behaviors observed.

Order parameters indicate phase transition phenomena.

Monte Carlo simulations validate the model's physical properties.

Abstract

A numerical investigation of a non-commutative field theory defined via the spectral action principle is conducted. The construction of this triple relies on an 8-dimensional Clifford algebra. Following to the standard procedure of non-commutative geometry, the spectral action is computed for the product of the triple (A,H,D) with a matrix-valued spectral triple. 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.