Color symmetry in the Potts spin glass at high temperature

Abstract

We show that color symmetry is preserved at high temperatures in the Potts spin glass model with $\kappa \ge 3$ colors. Our proof employs the second moment method applied to the balanced model with a suitable centering of the Hamiltonian, while incorporating results from the non-disordered Potts model Ellis--Wang (1990), https://doi.org/10.1016/0304-4149(90)90122-9. For $\kappa = 2$, we exploit the model's gauge symmetry to show that unbalanced configurations occur with exponentially small probability at all temperatures $\beta \in [0, \infty]$.