The BKT transition in low-dimensional systems with a U(1) global symmetry separates a gapless conformal phase from a trivially gapped, disordered phase, and is driven by vortex proliferation.
Recent developments in modified Villain discretizations provide a class of lattice models which have a ZW global symmetry that counts vortices mod W, mixed ’t Hooft anomalies, and persistent order even at finite lattice spacing.
While there is no fully-disordered phase (except in the original BKT limit W=1) there is still a phase boundary which separates gapped ordered phases from gapless phases. I’ll describe a numerical Monte Carlo exploration of these phenomena.
