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Europhysics Letters (EPL)

Phase Diagram for a Ferromagnetic System with Potts Symmetry in Four Dimensions

Sergio Caracciolo A, Giorgio Parisi A, Stefano Patarnello

Published Jul 1, 1987• 8 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/4/1/002

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Abstract The Wang–Landau algorithm of the Monte Carlo method is used to study the magnetic structures of the ground state, phase transitions, and thermodynamic properties of the two-dimensional antiferromagnetic Potts model with number q = 4 of spin states in a hexagonal lattice with the interactions of the nearest (J1) and next-to-nearest (J2) neighbors. The exchange interaction ratios in the range of 0.0 ≤ r = |J2/J1| ≤ 1.0 are studied. A phase diagram of the dependence of the critical temperature on the exchange interaction value of the next-to-nearest neighbors is constructed. The nature of phase transitions is analyzed. It is found that a first-order phase transition is observed in the range of 0.1 ≤ r ≤ 1.0, while there is no phase transition in the system and a strong degeneracy of the ground state is observed at r = 0.0.
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