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

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.