Fluctuations of topological charges in two-dimensional classical Heisenberg model

TL;DR

This study investigates the behavior of topological defects in the 2D classical Heisenberg model, revealing a temperature-dependent transition from defect binding to unbinding, similar to the Kosterlitz-Thouless transition.

Contribution

It introduces a novel analysis of skyrmion number fluctuations to characterize defect binding and unbinding in the 2D Heisenberg model, extending understanding beyond the XY model.

Findings

Fluctuation proportional to loop perimeter at low T

Fluctuation proportional to loop area at high T

Evidence of a defect unbinding transition

Abstract

Binding and unbinding of vortices drives Kosterlitz-Thouless phase transition in two-dimensional XY model. Here we investigate whether similar mechanism works in two-dimensional Heisenberg model, by using the fluctuation of skyrmion number inside a loop to characterize the nature of binding versus unbinding of defects. Through Monte Carlo simulations, we find that the fluctuation is proportional to the perimeter of the loop at low temperatures while it is proportional to the area of the loop at high temperatures, implying binding of the defects at low temperatures and unbinding at high temperatures.