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We study the critical behavior of the short-range p-state Potts spin glass inthree and four dimensions using Monte Carlo simulations. In three dimensions,for p = 3, a finite-size scaling analysis of the correlation length shows clearevidence of a transition to a spin-glass phase at T_c = 0.273(5) for a Gaussiandistribution of interactions and T_c = 0.377(5) for a bimodal distribution.These results indicate that the lower critical dimension of the 3-state Pottsglass is below three. By contrast, the correlation length of the ten-state (p =10) Potts glass in three dimensions remains small even at very low temperaturesand 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(3).Comment: 11 pages, 13 figures, 6 table

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