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arXiv · 1412.6588

Low temperature Glauber dynamics under weak competing interactions

M. D. Grynberg
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Abstract

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.

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M. D. Grynberg. 2015-03-04. Low temperature Glauber dynamics under weak competing interactions. https://doi.org/10.1103/physreve.91.032129

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