Sums of random matrices and the Potts model on random planar maps

We compute the partition function of the q-states Potts model on a random planar lattice with 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...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2016-05, Vol.49 (18), p.185201
Main Authors: Atkin, Max R, Niedner, Benjamin, Wheater, John F
Format: Article
Language:English
Subjects:
boundary condition
matrix model
Potts model
triangulation
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Summary:We compute the partition function of the q-states Potts model on a random planar lattice with 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 and comment on the conformal field theory description of the critical points.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/49/18/185201