Low temperature Glauber dynamics under weak competing interactions

We consider the low but nonzero temperature regimes of the Glauber dynamics in a chain of Ising spins with first and second neighbor interactions \(J_1,\, J_2\). For \(0 < -J_2 / | J_1 | < 1\) it is known that at \(T = 0\) the dynamics is both metastable and non-coarsening, while being always...

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Bibliographic Details
Published in:arXiv.org 2015-03
Main Author: Grynberg, M D
Format: Article
Language:English
Subjects:
Coarsening
Ising model
Online Access:Get full text
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Summary:We consider the low but nonzero temperature regimes of the Glauber dynamics in a chain of Ising spins with first and second neighbor interactions \(J_1,\, J_2\). For \(0 < -J_2 / | J_1 | < 1\) it is known that at \(T = 0\) the dynamics is both metastable and non-coarsening, while being always ergodic and coarsening in the limit of \(T \to 0^+\). Based on finite-size scaling analyses of relaxation times, here we argue that in that latter situation the asymptotic kinetics of small or weakly frustrated \(-J_2/ | J_1 |\) ratios is characterized by an almost ballistic dynamic exponent \(z \simeq 1.03(2)\) and arbitrarily slow velocities of growth. By contrast, for non-competing interactions the coarsening length scales are estimated to be almost diffusive.
ISSN:2331-8422
DOI:10.48550/arxiv.1412.6588