Phase diagrams of the multitrace quartic matrix models of noncommutative \Phi^4

TL;DR

This paper uses an exact Metropolis algorithm to accurately map the phase diagram of noncommutative ^2  theory on the fuzzy sphere, revealing detailed phase boundaries and critical behavior.

Contribution

It provides a robust, ergodic-problem-free calculation of the phase diagram, including the stripe transition, and confirms critical exponents match known Onsager values.

Findings

Reconstructed the entire phase diagram with boundaries and triple point.

Confirmed Ising transition critical exponents match Onsager values.

Located the triple point at (5, 0.4), consistent with previous estimates.

Abstract

We report a direct and robust calculation, free from ergodic problems, of the non-uniform-to-uniform (stripe) transition line of noncommutative $\Phi^4_2$ by means of an exact Metropolis algorithm applied to the first non-trivial multitrace correction of this theory on the fuzzy sphere. In fact, we reconstruct the entire phase diagram including the Ising, matrix and stripe boundaries together with the triple point. We also report that the measured critical exponents of the Ising transition line agrees with the Onsager values in two dimensions. The triple point is identified as a termination point of the one-cut-to-two-cut transition line and is located at $(\tilde{b},\tilde{c})=(-1.55,0.4)$ which compares favorably with previous Monte Carlo estimate.