Universality of the Berezinskii-Kosterlitz-Thouless type of phase transition in the dipolar XY-model

TL;DR

This paper demonstrates that a Berezinskii-Kosterlitz-Thouless (BKT) phase transition occurs in a dipolar XY-model, with the transition characterized by vortex-antivortex pair dissociation influenced by dipolar interactions and screening effects.

Contribution

It shows that the BKT transition is universal in dipolar XY-models and introduces a topological charge model to explain vortex screening and pair dissociation.

Findings

Transition temperature slightly higher than short-range BKT case

Screening alters vortex interaction from linear to logarithmic

Numerical simulations confirm the topological charge model

Abstract

We investigate the nature of the phase transition occurring in a planar XY-model spin system with dipole-dipole interactions. It is demonstrated that a Berezinskii-Kosterlitz-Thouless (BKT) type of phase transition always takes place at a finite temperature separating the ordered (ferro) and the disordered (para) phases. The low-temperature phase corresponds to an ordered state with thermal fluctuations, composed of a "gas" of bound vortex-antivortex pairs, which would, when considered isolated, be characterized by a constant vortex-antivortex attraction force which is due to the dipolar interaction term in the Hamiltonian. Using a topological charge model, we show that small bound pairs are easily polarized, and screen the vortex-antivortex interaction in sufficiently large pairs. Screening changes the linear attraction potential of vortices to a logarithmic one, and leads to the familiar pair dissociation mechanism of the BKT type phase transition. The topological charge model is confirmed by numerical simulations, in which we demonstrate that the transition temperature slightly increases when compared with the BKT result for short-range interactions.