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Non-trivial exponents in the zero temperature dynamics of the 1D Ising and Potts models

1994; Institute of Physics; Volume: 27; Issue: 11 Linguagem: Inglês

10.1088/0305-4470/27/11/002

1361-6447

Bernard Derrida, A. J. Bray, Claude Godrèche,

Stochastic processes and statistical mechanics

We consider the Glauber dynamics of the q-state Potts model in one dimension at zero temperature. Starting with a random initial configuration, we measure the density rt of spins which have never dipped from the beginning of the simulation until time t. We find that for large t, the density rt has a power-law decay (rt approximately t- theta ) where the exponent theta varies with q. Our simulations lead to theta approximately=0.37 for q=2, theta approximately=0.53 for q=3 and theta to 1 as q to infinity .