Berezinskii-Kosterlitz-Thouless transition through the eyes of duality

A new “bond-algebraic” approach to duality transformations provides a very powerful technique to analyze elementary excitations in the classical two-dimensional XY and p-clock models. By combining duality and Peierls arguments we establish the non-Abelian symmetries, phase structure and transitions of these models, unveil the nature of their topological excitations, and explicitly show the continuous U(1) symmetry that emerges when p ≥ 5. The latter is associated with the appearance of discrete vortices and Berezinskii-Kosterlitz-Thouless-type transitions.