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

L. W. Lee·Helmut G. Katzgraber·A. P. Young
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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).

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L. W. Lee, Helmut G. Katzgraber, A. P. Young. 2006-09-26. Critical behavior of the three- and ten-state short-range Potts glass: A Monte Carlo study. https://doi.org/10.1103/physrevb.74.104416

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