Topological Charge Order in a Frustrated XY Model and Related systems

Details Topological Charge Order in a Frustrated XY Model and Related systems Topological Charge Order in a Frustrated XY Model and Related systems

2001-07-16

arxiv.org/abs/cond-mat/0107339v4

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

We prove the existence of a finite temperature Z_{2} phase transition for the topological charge ordering within the Fully Frustrated XY Model. Our method enables a proof of the topological charge confinement within the conventional XY models from a rather general vista. One of the complications that we face is the non-exact equivalence of the continuous (angular) XY model and its discrete topological charge dual. In reality, the energy spectra of the various topological sectors are highly nested much unlike that suggested by the discrete dual models. We surmount these difficulties by exploiting the Reflection Positivity symmetry that this periodic flux phase model possesses. The techniques introuduced here may also be applied to examine transitions associated with other topological defects, e.g. the confinement of disclinations in the isotropic to nematic transition.

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