On the Phase Structure of Commuting Matrix Models

Abstract

We perform a systematic study of commutative $SO(p)$ invariant matrix models with quadratic and quartic potentials in the large $N$ limit. We find that the physics of these systems depends crucially on the number of matrices with a critical rôle played by $p=4$. For $p\le 4$ the system undergoes a phase transition accompanied by a topology change transition. For $p>4$ the system is always in the topologically non-trivial phase and the eigenvalue distribution is a Dirac delta function spherical shell. We verify our analytic work with Monte Carlo simulations.

37 pages, 13 figures, minor corrections, updated to match the published version

References in corpus (4)

• Fractional M2-branes
• Multi-matrix models and emergent geometry
• Geometry in transition: A model of emergent geometry
• A phase transition in commuting Gaussian multi-matrix models

Cited by in corpus (10)

• Lectures on Matrix Field Theory I
• On the transverse M5-branes in matrix theory
• Detecting scaling in phase transitions on the truncated Heisenberg algebra
• Spherical transverse M5-branes from the plane wave matrix model
• Higher spin JT gravity and a matrix model dual
• Approximate treatment of noncommutative curvature in quartic matrix model
• Geometry in transition in four dimensions: A model of emergent geometry in the early universe and dark energy
• Emergent fuzzy geometry and fuzzy physics in $4$ dimensions
• Commuting Quantum Matrix Models
• Phase transitions in a ${\Phi }^4$ matrix model on a curved noncommutative space