Monte Carlo study of the critical behavior of the two-dimensional biquadratic planar rotator model

Abstract

We present an analysis of the critical properties of the two-dimensional rigid rotor model with a biquadratic interaction $H=\ensuremath{-}J{\ensuremath{\sum}}_{i,j}{S}_{i}\ensuremath{\cdot}{S}_{j}+D{\ensuremath{\sum}}_{i,j}({S}_{i}\ensuremath{\cdot}{S}_{j}{)}^{2}.$ We use a self-consistent harmonic approximation and a Monte Carlo calculation to study the Hamiltonian. The results for the specific heat, susceptibility, fourth order Binder's cumulant and helicity modulus obtained by Monte Carlo suggest that the model has a critical BKT line $\ensuremath{-}\ensuremath{\infty}<D/J<{D}_{c}/J,$ where ${D}_{c}/J=0.96(9).citation$