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arXiv · 1511.03657

Sums of Random Matrices and the Potts Model on Random Planar Maps

Max R. Atkin·Benjamin Niedner·John F. Wheater
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Abstract

We compute the partition function of the $q$-states Potts model on a random planar lattice with $p\leq q$ allowed, equally weighted colours on a connected boundary. To this end, we employ its matrix model representation in the planar limit, generalising a result by Voiculescu for the addition of random matrices to a situation beyond free probability theory. We show that the partition functions with $p$ and $q-p$ colours on the boundary are related algebraically. Finally, we investigate the phase diagram of the model when $0\leq q\leq 4$ and comment on the conformal field theory description of the critical points.

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Max R. Atkin, Benjamin Niedner, John F. Wheater. 2015-12-03. Sums of Random Matrices and the Potts Model on Random Planar Maps. https://doi.org/10.1088/1751-8113%2F49%2F18%2F185201

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