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Physics Letters B

On the order of the phase transition in the 3D three-state Potts model with anti-ferromagnetic next-to-nearest neighbour coupling

Rajiv V. Gavai, F. Karsch

Published Dec 1, 1989• 9 citations
Publisher
DOI
10.1016/0370-2693(89)91333-6

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We performed a Monte Carlo simulation on a four-dimensional hypercube for the three-state Potts model with ferromagnetic nearest-neighbours interactions and antiferromagnetic next-nearest-neighbours interactions. We find that on the ferromagnetic branch of the critical line the phase transition is always of first order. This result, which is in agreement with Landau and mean-field theories, precludes the possibility of defining a continuum limit of the model and confirms the difficulties met in the construction of a four-dimensional nontrivial scalar field theory.
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.