Phase transitions in the Potts spin-glass model

We have studied the Potts spin glass with two-state Ising spins and $s$-state Potts variables using a cluster Monte Carlo dynamics. The model recovers the $\ifmmode\pm\else\textpm\fi{}J$ Ising spin glass (SG) for $s=1$ and exhibits for all $s$ a SG transition at ${T}_{\mathrm{SG}}(s)$ and a percolation transition at higher temperature ${T}_{p}(s).$ We have shown that for all values of $s\ensuremath{\ne}1$ at ${T}_{p}(s)$ there is a thermodynamic transition in the universality class of a ferromagnetic $s$-state Potts model. The efficiency of the cluster dynamics is compared with that of standard spin-flip dynamics.