Critical dynamics of the spin-exchange model in quasilinear fractal geometries

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Abstract
Comments on the dynamic critical exponents recently reported by Leyvraz and Jan (ibid., vol.19, p.603, 1986), in particular that for the spin-exchange kinetic Ising model in one dimension, z=3. This result is at variance with rigorous inequalities that z cannot be less than five for this model, i.e z>or=5. The source of the discrepancy appears to lie in the Monte Carlo algorithm which subsumes a critically slow dynamical process, leading to an apparently faster dynamics in the critical region. In addition, the author extends the finding for one dimension to the quasilinear (non-branching) fractal Koch curve, concluding z=3df, where df is the fractal dimension. He discusses the physical factors comprising the lower bound to the dynamic exponent in one dimension, z=5. He then obtains the generalised lower bound for spin-exchange dynamics of the non-branching Koch curve, z=3df+dw=5df, where dw is the random walk dimension.

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