# Low temperature Glauber dynamics under weak competing interactions

Source: [Low temperature Glauber dynamics under weak competing interactions](<https://www.sota2.com/research/paper/68fa2eac1e209131ce864f28>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T17:04:11.804Z

Authors: M. D. Grynberg

Published: 2014-12-20T03:16:13.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1412.6588>)

[PDF](<https://arxiv.org/pdf/1412.6588.pdf>)