ORDERING DYNAMICS OF MICROSCOPIC MODELS WITH NONCONSERVED ORDER-PARAMETER OF CONTINUOUS SYMMETRY

Numerical Monte Carlo temperature-quenching experiments have been performed on two three-dimensional classical lattice models with continuous ordering symmetry: the Lebwohl-Lasher model [Phys. Rev. A 6, 426 (1972)] and the ferromagnetic isotropic Heisenberg model. Both models describe a transition from a disordered phase to an orientationally ordered phase of continuous symmetry. The Lebwohl-Lasher model accounts for the orientational ordering properties of the nematic-isotropic transition in liquid crystals and the Heisenberg model for the ferromagnetic-paramagnetic transition in magnetic crystals. For both models, which have a nonconserved order parameter, it is found that the linear scale, R (t), of the evolving order, following quenches to below the transition temperature, grows at late times in an effectively algebraic fashion, R (t) approximately t(n), with exponent values which are strongly temperature dependent and furthermore vary for different measures of the time-dependent length scale. The results are discussed in relation to modern theories of ordering dynamics in systems with continuous order-parameter symmetry.