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Journal of Physics A Mathematical and General

Non-universality in the dynamics of the one-dimensional Potts model

P. O. Weir, J. Michael Kosterlitz, Steve Adachi

Published Aug 21, 1986• 12 citations
Publisher

Abstract

The authors discuss two recent papers on the dynamics of the one-dimensional Potts model which yield different values of the dynamical critical exponent. They show that in fact there are choices of the transition rates which yield arbitrarily large non-universal exponents.
DOI
10.1088/0305-4470/19/12/011

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The one-dimensional kinetic Potts models are studied for both Glauber and Kawasaki dynamics with different transition rates. Rigorous lower bounds for the dynamical exponent (z) are obtained from the initial response rate and the scaling hypothesis for the relaxation time. It is shown that the z exponent is non-universal for several periodic models with a basic unit cell (J 1 ,J 2 ,. . .,JM) containing different coupling constants. The critical dynamics of the alternating bond model is also studied by a simple argument about the movement of domain walls.
Recent results concerning non-universality in the dynamical critical behavior of the one-dimensional Ising model, are generalised to several formulations of the Potts model, using arguments based on domain wall motion. By applying real-space renormalisation group methods, the authors also study the dynamical Ising model, with single flips, both for a period distribution of nearest-neighbor exchanges and for the random chain (with nonzero couplings). They show that the critical dynamical exponent is z=1+J M /J m where J M (J m ) is the greatest (smallest) of the exchanges.