Matrix geometries and Matrix Models

TL;DR

This paper investigates a two-parameter 3-matrix model with SO(3) symmetry, revealing two distinct phases, analyzing phase transitions, and examining eigenvalue distributions to understand the model's geometric and physical properties.

Contribution

It introduces a detailed analysis of phase behavior and eigenvalue distributions in a two-parameter 3-matrix model with SO(3) symmetry, highlighting novel phase transition characteristics.

Findings

Identification of fuzzy sphere and matrix phases.

Evidence of two distinct phase transition behaviors.

Eigenvalue distributions consistent with theoretical expectations.

Abstract

We study a two parameter single trace 3-matrix model with SO(3) global symmetry. The model has two phases, a fuzzy sphere phase and a matrix phase. Configurations in the matrix phase are consistent with fluctuations around a background of commuting matrices whose eigenvalues are confined to the interior of a ball of radius R=2.0. We study the co-existence curve of the model and find evidence that it has two distinct portions one with a discontinuous internal energy yet critical fluctuations of the specific heat but only on the low temperature side of the transition and the other portion has a continuous internal energy with a discontinuous specific heat of finite jump. We study in detail the eigenvalue distributions of different observables.