Why the anisotropic planar rotor model is nearly second order

Scott T. Milner, Amalie L. Frischknecht
2001 Journal of Chemical Physics  
Despite extensive Monte Carlo ͑MC͒ simulations, the nature of the phase transition in the anisotropic planar rotor ͑APR͒ model remains elusive. The ground state is sixfold degenerate, which would naively suggest strongly first-order qϭ6 Potts behavior. Extensive MC simulations indicate either a second-order transition with qϭ3 Potts exponents, or a very weakly first-order transition. We show that the APR model maps to a generalized six-state Potts model, with a bond energy between pairs of
more » ... states q and (qϩ3) mod 6 larger by a factor ␣ϭ␣ APR у2. For ␣ϭ␣ T Ϸ2.5, there exists a tricritical point separating first-order behavior ͑including qϭ6 Potts at ␣ϭ1͒ from second-order behavior ͑including qϭ3 Potts at large ␣͒. Thus the APR model is weakly first order because of the proximity to this tricritical point.
doi:10.1063/1.1367285 fatcat:6fjmgteas5cxlfvrovzr7ta2cy