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Exact Persistence Exponent for One-dimensional Potts Models with Parallel Dynamics

Gautam I. Menon·P. Ray
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Abstract

We obtain θ_p(q) = 2θ_s(q) for one-dimensional q-state ferromagnetic Potts models evolving under parallel dynamics at zero temperature from an initially disordered state, where θ_p(q) is the persistence exponent for parallel dynamics and θ_s(q) = -{1/8}+ \frac{2}{π^2}[cos^{-1}{(2-q)/q\sqrt{2}}]^2 [PRL, {\bf 75}, 751, (1995)], the persistence exponent under serial dynamics. This result is a consequence of an exact, albeit non-trivial, mapping of the evolution of configurations of Potts spins under parallel dynamics to the dynamics of two decoupled reaction diffusion systems.

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Gautam I. Menon, P. Ray. 2001-11-01. Exact Persistence Exponent for One-dimensional Potts Models with Parallel Dynamics. https://doi.org/10.1088/0305-4470%2F34%2F50%2F102

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