Coarsening Dynamics of an Antiferromagnetic XY model on the Kagome Lattice: Breakdown of the Critical Dynamic Scaling

TL;DR

This paper investigates the coarsening dynamics of an antiferromagnetic XY model on the kagome lattice, revealing a breakdown of critical dynamic scaling and complex vortex decay behavior during phase ordering.

Contribution

It uncovers the failure of dynamic scaling laws and identifies multiple length scales with nontrivial relations in the model's low-temperature phase.

Findings

Multiple growing length scales are identified.

Quasi-ordered domain growth exhibits anomalous, non-power-law behavior.

Vortex decay follows an exponential of a logarithmic power law.

Abstract

We find a breakdown of the critical dynamic scaling in the coarsening dynamics of an antiferromagnetic {\em XY} model on the kagome lattice when the system is quenched from disordered states into the Kosterlitz-Thouless ({\em KT}) phases at low temperatures. There exist multiple growing length scales: the length scales of the average separation between fractional vortices are found to be {\em not} proportional to the length scales of the quasi-ordered domains. They are instead related through a nontrivial power-law relation. The length scale of the quasi-ordered domains (as determined from optimal collapse of the correlation functions for the order parameter $\exp[3 i \theta (r)]$) does not follow a simple power law growth but exhibits an anomalous growth with time-dependent effective growth exponent. The breakdown of the critical dynamic scaling is accompanied by unusual relaxation dynamics in the decay of fractional ($3\theta$) vortices, where the decay of the vortex numbers is characterized by an exponential function of logarithmic powers in time.