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

9 pages of RevTex4-1, 4 figures

References in corpus (8)

• Condensed Matter Theory of Dipolar Quantum Gases
• Strongly Correlated Quantum Fluids: Ultracold Quantum Gases, Quantum Chromodynamic Plasmas, and Holographic Duality
• Critical Point of an Interacting Two-Dimensional Atomic Bose Gas
• Heteronuclear molecules in an optical dipole trap
• Strongly Interacting Two-Dimensional Bose Gases
• Critical Binder cumulant of two-dimensional Ising models
• Phase transition in ultrathin magnetic films with long-range interactions: Monte Carlo simulation of the anisotropic Heisenberg model
• Phase Transition of XY Model in Heptagonal Lattice

Cited by in corpus (6)

• Long-range interacting quantum systems
• Half-Quantum Vortex Molecules in a Binary Dipolar Bose Gas
• $BKT$ transitions in classical and quantum long-range systems
• Quantum Geometric Exciton Drift Velocity
• Villain model with long-range couplings
• Berezinskii-Kosterlitz-Thouless phase transitions with long-range couplings