Why the anisotropic planar rotor model is nearly second order

摘要: Despite extensive Monte Carlo (MC) simulations, the nature of phase transition in anisotropic planar rotor (APR) model remains elusive. The ground state is sixfold degenerate, which would naively suggest strongly first-order q=6 Potts behavior. Extensive MC simulations indicate either a second-order with q=3 exponents, or very weakly transition. We show that APR maps to generalized six-state model, bond energy between pairs states q and (q+3) mod 6 larger by factor α=αAPR⩾2. For α=αT≈2.5, there exists tricritical point separating behavior (including at α=1) from large α). Thus first order because proximity this point.