Non-trivial exponents in the zero temperature dynamics of the 1D Ising and Potts models
Résumé
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 $ r_t $ of spins which have never flipped from the beginning of the simulation until time $ t. $ We find that for large $ t, $ the density $ r_t $ has a power law decay $ \left(r_t \sim t^{-\theta} \right) $ where the exponent $ \theta $ varies with $ q. $ Our simulations lead to $ \theta \simeq .37 $ for $ q=2, $ $ \theta \simeq .53 $ for $ q=3 $ and $ \theta \longrightarrow 1 $ as $ q \longrightarrow \infty . $
Domaines
Physique Générale [physics.gen-ph]
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