Abstract
We study vortex unbinding for the classical two-dimensional XY model in a magnetic field on square and triangular lattices. A renormalization group analysis combined with duality in the model shows that at high temperature and high field, the vortices unbind as the magnetic field is lowered in a two-step process: strings of overturned spins first proliferate and then vortices unbind. The transitions are highly continuous but are not of the Kosterlitz–Thouless type. The unbound vortex fixed point is shown to inherit properties of the underlying lattice, in particular containing a set of nodal lines that reflect the lattice symmetry.
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