Unbinding of giant vortices in states of competing order

Abstract

We consider a two-dimensional system with two order parameters, one with O(2) symmetry and one with O($M$), near a point in parameter space where they couple to become a single O($2+M$) order. While the O(2) sector supports vortex excitations, these vortices must somehow disappear as the high symmetry point is approached. We develop a variational argument which shows that the size of the vortex cores diverges as $1/\sqrt{\Delta }$ and the Berezinskii-Kosterlitz-Thouless transition temperature of the O(2) order vanishes as $1/\ln (1/\Delta )$, where $\Delta$ denotes the distance from the high-symmetry point. Our physical picture is confirmed by a renormalization group analysis which gives further logarithmic corrections, and demonstrates full symmetry restoration within the cores.

arXiv comment4.5 pages, 2 figures; expanded discussion of BKT transition with two length scales

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