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

Lee, L. W.; Katzgraber, Helmut G.; Young, A. P.

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

Authors

Lee, L. W.

Katzgraber, Helmut G.

Young, A. P.

Description

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(5) for a Gaussian distribution of interactions and T_c = 0.377(5) for a bimodal distribution. These results indicate that the lower critical dimension of the 3-state Potts glass 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 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(3).
11 pages, 13 figures, 6 tables