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Topological-Charge Fluctuations and KT-like Transition in the 2D Classical Heisenberg Model

Using the loop fluctuation (variance) of the discretized topological (skyrmion) charge as an order-parameter-like diagnostic that distinguishes bound from free topological defects via perimeter-law versus area-law scaling, and using Metropolis Monte Carlo to show that unprotected skyrmion fragments can drive a Kosterlitz-Thouless-like transition in the 2D classical Heisenberg model.

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Fluctuations of topological charges in two- dimensional classical Heisenberg model Shan-Chang

This physics research Letter asks whether the binding/unbinding mechanism behind the Kosterlitz-Thouless (KT) transition in the 2D XY model also operates in the 2D classical O(3) Heisenberg model, ev…