Dynamic scaling near the Kasteleyn transition in spin ice: critical relaxation of monopoles and strings following a field quench

TL;DR

This paper investigates the critical relaxation dynamics of monopoles and strings in spin ice after a magnetic field quench near the Kasteleyn transition, using simulations and scaling theory.

Contribution

It introduces a solvable stochastic model based on independent strings that accurately describes relaxation and string length distribution near the critical point.

Findings

String-based stochastic model matches simulation results

Scaling forms describe behavior over a range of monopole densities

Breakdown of scaling understood away from criticality

Abstract

We study dynamics in classical spin ice following a magnetic field quench to close to the Kasteleyn transition, using Monte Carlo simulations and dynamic scaling theory to characterize the relaxation of the magnetization and the density of magnetic monopoles. We have previously argued that this dynamics can be described in terms of seeding and growth of strings of flipped spins, and our results here demonstrate that a solvable stochastic model based on independent strings correctly describes the relaxation as well as the distribution of string lengths within the critical scaling regime near the transition. We also show how generalized scaling forms capture the behavior over a broader range of monopole densities and provide a clear understanding of the breakdown of the scaling picture further from the critical point.