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

Numerical Monte Carlo temperature-quenching experiments have been perf ormed on two three-dimensional classical lattice models with continuou s ordering symmetry: the Lebwohl-Lasher model [Phys. Rev. A 6, 426 (19 72)] and the ferromagnetic isotropic Heisenberg model. Both models des cribe a transition from a disordered phase to an orientationally order ed phase of continuous symmetry. The Lebwohl-Lasher model accounts for the orientational ordering properties of the nematic-isotropic transi tion 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 transi tion temperature, grows at late times in an effectively algebraic fash ion, 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 or der-parameter symmetry.