Abstract
We study the -state Potts model with four-site interaction on a square lattice. Based on the asymptotic behavior of lattice animals, it is argued that when the system exhibits a second-order phase transition and when the transition is first order. The model is borderline. We find to be an upper bound on , the exact critical temperature. Using a low-temperature expansion, we show that , where is a -dependent geometrical term, is an improved upper bound on . In fact, our findings support . This expression is used to estimate the finite correlation length in first-order transition systems. These results can be extended to other lattices. Our theoretical predictions are confirmed numerically by an extensive study of the four-site interaction model using the Wang-Landau entropic sampling method for . In particular, the model shows an ambiguous finite-size pseudocritical behavior.
- Received 3 August 2017
DOI:https://doi.org/10.1103/PhysRevE.97.032106
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