The Study on the Phase Transitional Property of an Extended Three-State Potts Model

Abstract: Three-state Potts model has been great interesting to the theoretical physicists, as itbelongs to the same universal class with a few kinds of material with superconductivityor superfluidity. It is significant to study its transitional property of Three-state Pottsmodel. Although people have got comparatively a good knowledge about the phasetransitional property the ferromagnetic Three—state Potts model, and knew some thingabout the antiferromagnetic ones, however, there are still many inconsistent results andproblems have not been solved yet in this area, such as the identifying the transitionclass of the antiferromagnetic Three-state Potts model; the searching for the tricriticalpoints between the first and second order transition, finding the critical behavior of thetricritical points etc., , on which worth us to make deep study, In this article we use Monte Carlo Method study the transitional property ofextended three-state potts and the process of changing from the antiferromagneticthree-state Potts Model to the Model on triangle lattice and the ferromagnetic one,according to scaling theory. We have obtained the three dimensional phase diagram forthis system; and we find that the there is a tricritical point between the first and secondorder transition area along a special line at (0.025,2.975) in the phase space, thecritical exponents at this tricritical point have also been calculated. The result is thatν = 0.85±0.06,β = 0.11±0.04.These results are significant for the further study of thetransition property of the Three-state Potts model on triangle lattice as well as for thestudy of the material with superfluidity or superconductivity…
Key words: Monte Carlo Method; Extended Three-State Potts Model; Tricritical Point; Critical Exponent.

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