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)∼${\mathit{t}}^{\mathit{n}}$, 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.