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

Abstract

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).

arXiv comment11 pages, 13 figures, 6 tables

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• Disordered Potts model on the diamond hierarchical lattice: Numerically exact treatment in the large-q limit
• Strange Attractor in the Potts Spin Glass on Hierarchical Lattices
• Evidence of one-step replica symmetry breaking in a three-dimensional Potts glass model
• Locally self-similar phase diagram of the disordered Potts model on the hierarchical lattice
• Evidence of a glass transition in a 10-state non-mean-field Potts glass
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