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}
}

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