Exact exponent for the number of persistent spins in the zero-temperature dynamics of the one-dimensional Potts model |
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Authors: | Bernard Derrida Vincent Hakim Vincent Pasquier |
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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 |
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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)t
–(q)
when the initial condition is random. By mapping the problem onto an exactly soluble one-species coagulation model (A+AA) or alternatively by transforming the problem into a free-fermion model, we obtain the exact expression of (q) for all values ofq. The exponent (q) is in general irrational, (3)=0.53795082..., (4)=0.63151575..., ..., with the exception ofq=2 andq=, for which (2)=3/8 and ()=1. |
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Keywords: | Glauber dynamics coarsening free fermions Toeplitz determinant Potts model reaction-diffusion problems |
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