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Physical Review A

Kawasaki dynamics in the Ising chain with mixed interactions

J. M. Nunes da Silva, Eduardo Lage

Published Oct 1, 1989• 6 citations
Publisher

Abstract

The renormalization-group method recently applied to Kawasaki dynamics in the Ising chain is generalized to periodically distributed interactions. Our results confirm those recently obtained by a different technique, for the special case of alternating interactions. However, our method can be applied to the general one-dimensional situation, with arbitrary periods.

DOI
10.1103/physreva.40.4682

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The renormalization-group method recently applied to Kawasaki dynamics in the Ising chain is generalized to periodically distributed interactions. Our results confirm those recently obtained by a different technique, for the special case of alternating interactions. However, our method can be applied to the general one-dimensional situation, with arbitrary periods.
The dynamic Monte Carlo renormalization group is applied to the two-dimensional Kawasaki and three-dimensional Glauber models. Our best "matching" results for the Kawasaki model yield a value of z=3.80z=3.80z=3.80 for the dynamical exponent, as compared with the exact value z=3.75z=3.75z=3.75. This provides strong confirmation for the validity of this method. The results for the Glauber model are less accurate, but our estimate of $z\ensuremath{\simeq}2.08$ is in reasonable agreement with the $\ensuremath{\epsilon}$ expansion.