Asymmetric hermitian matrix models and fuzzy field theory

Abstract

We analyze two types of hermitian matrix models with asymmetric solutions. One type breaks the symmetry explicitly with an asymmetric quartic potential. We give the phase diagram of this model with two different phase transitions between the one cut and two cut solutions. The second type, describing real scalar field theory on fuzzy spaces, breaks the symmetry spontaneously with multitrace terms. We present two methods to study this model, one direct and one using a connection with the first type of models. We analyze the model for the fuzzy sphere and obtain a phase diagram with the location of the triple point in a good agreement with the most recent numerical simulations.

v3: minor changes in formulations, few typos corrected

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• Triple Point of a Scalar Field Theory on a Fuzzy Sphere
• Detecting scaling in phase transitions on the truncated Heisenberg algebra
• Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
• Approximate treatment of noncommutative curvature in quartic matrix model
• Beyond second-moment approximation in fuzzy-field-theory-like matrix models
• Phase transitions in a ${\Phi }^4$ matrix model on a curved noncommutative space
• Fuzzy field theories and related matrix models
• Eigenvalue-flipping Algorithm for Matrix Monte Carlo