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 ≤ 4 the system undergoes a phase transition accompanied by a topology change transition. For p > 4 the system is always in the topologically trivial phase and the eigenvalue distribution is a Dirac delta function spherical shell. We verify our analytic work with Monte Carlo simulations.
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Filev, V.G., O’Connor, D. On the phase structure of commuting matrix models. J. High Energ. Phys. 2014, 3 (2014). https://doi.org/10.1007/JHEP08(2014)003
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DOI: https://doi.org/10.1007/JHEP08(2014)003