Critical density of topological defects upon a continuous phase transition

Using extensive Monte Carlo simulations, we test the hypothesis that the density of corresponding topological defects has an universal value at the temperature of a continuous phase transition. We consider several simple two-dimensional models where domain walls, vortices, so-called $\mathbb{Z}_2$ vortices or their combinations are presented. These topological defects are relevant correspondingly to an Ising second-order phase transition, a Berezinskii-Kosterlitz Thouless transition and an explicit crossover. We compare results for square and triangular lattices as well as for the complicated situation when two types of defects are presented and two transitions occur separated in temperature. All considered cases demonstrate consentient results confirming the hypothesis.

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