Critical behavior of the three- and ten-state short-range Potts glass: A Monte Carlo study

We study the critical behavior of the short-range p-state Potts spin glass in three and four dimensions using Monte Carlo simulations. In three dimensions, for p=3, a finite-size scaling analysis of the correlation length shows clear evidence of a transition to a spin-glass phase at T_c≃0.273 for a Gaussian distribution of interactions and T_c≃0.377 for a ±J (bimodal) distribution. These results indicate that the lower critical dimension of the three-state Potts glass is below 3. By contrast, the correlation length of the ten-state (p=10) Potts glass in three dimensions remains small even at very low temperatures and thus shows no sign of a transition. In four dimensions we find that the p=3 Potts glass with Gaussian interactions has a spin-glass transition at T_c≃0.536.