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Exact exponent for the number of persistent spins in the zero-temperature dynamics of the one-dimensional Potts model
Authors:Bernard Derrida  Vincent Hakim  Vincent Pasquier
Institution:(1) Laboratoire de Physique Statistique, ENS, F-75231 Paris Cedex 05, France;(2) Service de Physique Théorique, CE Saclay, F-91191 Gif sur Yvette, France
Abstract:For the zero-temperature Glauber dynamics of theq-state Potts model, the fractionr(q, t) of spins which never flip up to timet decays like a power lawr(q, t)simt theta(q) when the initial condition is random. By mapping the problem onto an exactly soluble one-species coagulation model (A+ArarrA) or alternatively by transforming the problem into a free-fermion model, we obtain the exact expression of theta(q) for all values ofq. The exponent pgr(q) is in general irrational, theta(3)=0.53795082..., theta(4)=0.63151575..., ..., with the exception ofq=2 andq=infin, for which theta(2)=3/8 and theta(infin)=1.
Keywords:Glauber dynamics  coarsening  free fermions  Toeplitz determinant  Potts model  reaction-diffusion problems
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