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Slow Coarsening in an Ising Chain with Competing Interactions

S. Redner·P. L. Krapivsky
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Abstract

We investigate the zero-temperature coarsening dynamics of a chain of Ising spins with a nearest-neighbor ferromagnetic and an nth-neighbor antiferromagnetic interactions. For sufficiently large antiferromagnetic interaction, the ground state consists of $n$ consecutive up spins followed by n down spins, etc. We show that the asymptotic coarsening into this ground state is governed by a multispecies reactive gas of elementary excitations. The basic elementary excitations are identified and each decays at a different power-law rate in time. The dominant excitations are domains of n+1 spins which diffuse freely and disappear through processes which are effectively governed by (n+1)-particle annihilation. This implies that the ground state is approached slowly with time, as t^{-1/n}.

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S. Redner, P. L. Krapivsky. 1998-05-28. Slow Coarsening in an Ising Chain with Competing Interactions. https://doi.org/10.1088/0305-4470%2F31%2F46%2F013

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