Abstract
Monte Carlo (MC) simulations on the square planar rotator model with small fourfold symmetry-breaking field ${h}_{4}$ points out the existence of a Berezinskii-Kosterlitz-Thouless phase at intermediate temperatures between the low-temperature ferromagnetic phase and the high-temperature paramagnetic phase. This result contrasts with the expectation of a single order-disorer phase transition characterized by nonuniversal critical exponents for any ${h}_{4}$ as suggested by a renormalization group analysis and confirmed by MC simulations for intermediate and large symmetry-breaking fields.
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