Phase diagrams of the multitrace quartic matrix models of noncommutative Φ^4

Abstract

We report a direct and robust calculation, free from ergodic problems, of the non-uniform-to-uniform (stripe) transition line of noncommutative ${\Phi }_2^4$ 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.

30 pages, 4 tables, 7 figures (17 graphs). arXiv admin note: text overlap with arXiv:1410.4881. text overlap with arXiv:1410.4881

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Cited by in corpus (10)

• Lectures on Matrix Field Theory I
• Triple Point of a Scalar Field Theory on a Fuzzy Sphere
• Matrix model approximations of fuzzy scalar field theories and their phase diagrams
• Detecting scaling in phase transitions on the truncated Heisenberg algebra
• Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
• Quantum Gravity as a Multitrace Matrix Model
• The multitrace matrix model: An alternative to Connes NCG and IKKT model
• Beyond second-moment approximation in fuzzy-field-theory-like matrix models
• Wilsonian Matrix Renormalization Group
• Matrix Models of Fuzzy Field Theories