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

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