Dualities and the phase diagram of the $p$-clock model

Details Dualities and the phase diagram of the $p$-clock model Dualities and the phase diagram of the $p$-clock model

2011-08-10

arxiv.org/abs/1108.2276v1

Physics

Condensed Matter

Statistical Mechanics

48 pages, 5 figures. Submitted to Nuclear Physics B

Scientific paper

10.1016/j.nuclphysb.2011.09.012

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 existence of non-Abelian symmetries, the phase structure, and transitions of these models, unveil the nature of their topological excitations, and explicitly show that a continuous U(1) symmetry emerges when $p \geq 5$. This latter symmetry is associated with the appearance of discrete vortices and Berezinskii-Kosterlitz-Thouless-type transitions. We derive a correlation inequality to prove that the intermediate phase, appearing for $p\geq 5$, is critical (massless) with decaying power-law correlations.

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