The Phase Diagram of an Anisotropic Potts Model

Details The Phase Diagram of an Anisotropic Potts Model The Phase Diagram of an Anisotropic Potts Model

2005-01-25

arxiv.org/abs/cond-mat/0501604v2

J. Phys. A: Math. Gen. 38 (2005) 4047-4067

Physics

Condensed Matter

Statistical Mechanics

30 pages, 19 figures, one table

Scientific paper

10.1088/0305-4470/38/19/001

A study is made of an anisotropic Potts model in three dimensions where the coupling depends on both the Potts state on each site but also the direction of the bond between them using both analytical and numerical methods. The phase diagram is mapped out for all values of the exchange interactions. Six distinct phases are identified. Monte Carlo simulations have been used to obtain the order parameter and the values for the energy and entropy in the ground state and also the transition temperatures. Excellent agreement is found between the simulated and analytic results. We find one region where there are two phase transitions with the lines meeting in a triple point. The orbital ordering that occurs in $LaMnO_3$ occurs as one of the ordered phases.

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