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

@article{Atkin2016SumsOR,
  title={Sums of Random Matrices and the Potts Model on Random Planar Maps},
  author={Max R. Atkin and Benjamin Niedner and J. Wheater},
  journal={Journal of Physics A},
  year={2016},
  volume={49},
  pages={185201}
}
  • Max R. Atkin, Benjamin Niedner, J. Wheater
  • Published 2016
  • Mathematics, Physics
  • Journal of Physics A
  • 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… CONTINUE READING
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