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The European Physical Journal B

Slowing down in the three-dimensional three-state Potts glass with nearest neighbor exchange : A Monte Carlo study

M. Reuhl, P. Nielaba, Kurt Binder

Published May 1, 1998• 5 citations
Publisher
DOI
10.1007/s100510050244

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Results of Monte Carlo studies of the qqq-state Potts model on a square lattice with antiferromagnetic nearest-neighbor coupling and ferromagnetic next-nearest-neighbor coupling are presented for q> 3q>~3q> 3. The three-state Potts model shows a variety of unusual transitions whereas for q> 4q>~4q> 4, we find two first-order phase transitions separated by a broken sublattice symmetry state.
We investigate the phase transition of the three-state Potts model in an analytical approach—the generalized cumulant expansion with the effective mean field hypothesis. We find a first order phase transition in the three-dimensional three-state Potts model with ferromagnetic nearest neighbor coupling. For the model with antiferromagnetic next-to-nearest neighbor coupling, we find a first order transition when the relative strength of the -coupling is fixed to . The critical values given by this method are also in agreement with the recent high statistics Monte Carlo results.