Z. Zhang et al., ORDERING DYNAMICS OF MICROSCOPIC MODELS WITH NONCONSERVED ORDER-PARAMETER OF CONTINUOUS SYMMETRY, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 48(4), 1993, pp. 2842-2849
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.