Monte Carlo simulation of a planar rotator model with symmetry-breaking fields

The phase diagram and the critical behavior of the planar rotator model on square lattice with fourfold and on triangular lattice with sixfold symmetry-breaking field is obtained by Monte Carlo simulation. On the basis of a renormalization-group analysis the planar model with a fourfold symmetry-breaking field is expected to undergo a continuous phase transition with unconventional field dependent critical exponents, while the same model with sixfold symmetry-breaking field is expected to exhibit two phase transitions: a ferromagnetic-BKT (Berezinskii-Kosterlitz-Thouless) one at low temperature followed by a BKT-paramagnetic phase transition at high temperature. Both these expectations are confirmed by Monte Carlo simulations.