We present preliminary simulation results of the lattice sine-Gordon model which show evidence of the Berezinskii-Kosterlitz-Thouless phase transition. Our simulation algorithm uses Fourier accelerated hybrid Monte Carlo techniques to reduce autocorrelations. The BKT transition involves a topological phase, with no local order parameter, driven by the physics of topological defects. The sine-Gordon model captures the essential physics of vortices in the XY model and is dual to a two-dimensional Coulomb gas. Our work further validates earlier work of Hasenbusch et al. (1994), and extends the study to include other thermodynamic quantities and regions of parameter space, including some quantitative results on the critical line t_c(y), where y is the vortex fugacity and t_c is the critical temperature of the roughening transition.

Applications Beyond QCD