A Multitrace Approach to Noncommutative \Phi_2^4

TL;DR

This paper analyzes noncommutative ^4 theory on fuzzy sphere and Moyal-Weyl plane using multitrace methods, providing analytical predictions for phase transitions and comparing them with Monte Carlo results.

Contribution

It introduces a multitrace matrix model approach to analyze phase transitions in noncommutative ^4 theory, including a closed-form solution for the symmetric doubletrace model.

Findings

Closed-form solution for the symmetric doubletrace matrix model.

Analytical prediction of phase transition points.

Comparison with Monte Carlo measurements confirms the analysis.

Abstract

In this article we provide a multitrace analysis of the theory of noncommutative $\Phi^4$ in two dimensions on the fuzzy sphere ${\bf S}^2_{N,\Omega}$, and on the Moyal-Weyl plane ${\bf R}^{2}_{\theta, \Omega}$, with a non-zero harmonic oscillator term added. The doubletrace matrix model symmetric under $M\longrightarrow -M$ is solved in closed form. An analytical prediction for the disordered-to-non-uniform-ordered phase transition and an estimation of the triple point, from the termination point of the critical boundary, are derived and compared with previous Monte Carlo measurement.