Kosterlitz-Thouless transition of magnetic dipoles on the two-dimensional plane

Abstract

The universality class of a phase transition is often determined by factors like dimensionality and inherent symmetry. We study the magnetic dipole system in which the ground-state symmetry and the underlying lattice structure are coupled to each other in an intricate way. A two-dimensional (2D) square-lattice system of magnetic dipoles undergoes an order-disorder phase transition belonging to the 2D Ising universality class. According to Prakash and Henley [Phys. Rev. B {\bf 42}, 6572 (1990)], this can be related to the fourfold-symmetric ground states which suggests a similarity to the four-state clock model. Provided that this type of symmetry connection holds true, the magnetic dipoles on a honeycomb lattice, which possess sixfold-symmetric ground states, should exhibit a Kosterlitz-Thouless transition in accordance with the six-state clock model. This is verified through numerical simulations in the present investigation. However, it is pointed out that this symmetry argument does not always apply, which suggests that factors other than symmetry can be decisive for the universality class of the magnetic dipole system.

10 pages, 12 figures. to appear in Phys. Rev. B

References in corpus (4)

• Artificial "spin ice" in a geometrically frustrated lattice of nanoscale ferromagnetic islands
• Non-Kosterlitz-Thouless transitions for the $q$-state clock models
• True and quasi long-range order in the generalized $q$-state clock model
• Comment on `Six-state clock model on the square lattice: Fisher zero approach with Wang-Landau sampling'

Cited by in corpus (5)

• Phase diagram of dipolar-coupled XY moments on disordered square lattices
• Universality of the Berezinskii-Kosterlitz-Thouless type of phase transition in the dipolar XY-model
• Continuous ground-state degeneracy of classical dipoles on regular lattices
• Emergent tri-criticality in magnetic metamaterials
• Comparison of the clock, stochastic cutoff, and Tomita Monte Carlo methods in simulating the dipolar triangular lattice at criticality