Low temperature Glauber dynamics under weak competing interactions

TL;DR

This paper investigates the low-temperature Glauber dynamics of Ising spin chains with competing interactions, revealing near-ballistic behavior for weak frustration and diffusive coarsening for non-competing interactions.

Contribution

It provides a finite-size scaling analysis showing almost ballistic kinetics in weakly frustrated regimes, a novel insight into the dynamics of such spin systems.

Findings

Near-ballistic dynamic exponent z ≈ 1.03 for weak frustration

Arbitrarily slow growth velocities in weakly frustrated regimes

Diffusive coarsening length scales for non-competing interactions

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.