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

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.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1088/1751-8113/49/18/185201

Authors

More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Physics
Sub department:
Theoretical Physics
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Physics
Sub department:
Theoretical Physics
Role:
Author

Publisher:
IOP Publishing
Journal:
Journal of Physics A: Mathematical and Theoretical More from this journal
Volume:
49
Issue:
18
Article number:
185201
Publication date:
2016-01-01
Acceptance date:
2016-02-29
DOI:
EISSN:
1751-8121
ISSN:
1751-8113

Keywords:
Pubs id:
pubs:574392
UUID:
uuid:9b32be5f-2f7e-412d-b65f-9290bb0c8616
Local pid:
pubs:574392
Source identifiers:
574392
Deposit date:
2016-02-29

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