Dynamical Multiscaling in Quenched Skyrme Systems

TL;DR

This paper investigates the complex dynamical multiscaling behavior in quenched two-dimensional Skyrme systems with topologically stable skyrmions, revealing different decay behaviors depending on skyrmion stability.

Contribution

It introduces a simple two-length-scale model explaining multiscaling exponents when skyrmions expand, highlighting the role of skyrmion stability in dynamical scaling violations.

Findings

Dramatic differences in multiscaling spectra based on skyrmion stability.

A simple model successfully explains exponents during skyrmion expansion.

No simple model found for skyrmion shrinking cases.

Abstract

Strong dynamical scaling violations exist in quenched two-dimensional systems with vector O(3) order parameters. These systems support non-singular topologically stable configurations (skyrmions). By tuning the stability of isolated skyrmions to expand or shrink, we find dramatic differences in the dynamical multiscaling spectrum of decaying moments $< |\rho|^n >$ of the topological charge density distribution and in particular in the decay of the energy-density $\epsilon \sim < |\rho| >$. We present a simple two-length-scale model for the observed exponents in the case when isolated skyrmions expand. No such simple model is found when isolated skyrmions shrink.