Abstract
We formulate a theory of single-spin-flip dynamics for the infinite-rangeq-state Potts model. We derive a Fokker-Planck equation, without diffusive term, from a phenomenological master equation. It describes the approach to equilibrium of the time-dependent probability density and thus generalizes Griffiths' (1966) result for the Ising model. We particularly compare the dynamic evolutions ofq=2 andq=3 systems when sinusoidal external fields are applied. In the caseq=2 we find evidence of a nonequilibrium phase transition and forq=3 period doubling bifurcations are observed, yielding a good estimate of Feigenbaum's universal exponent.
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Mendes, J.F.F., Lage, E.J.S. Dynamics of the infinite-ranged Potts model. J Stat Phys 64, 653–672 (1991). https://doi.org/10.1007/BF01048310
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DOI: https://doi.org/10.1007/BF01048310