Anisotropy-induced crossover in domain growth kinetics

Abstract

We study the growth of order following a zero temperature quench in a conserved two-dimensional isotropic model, in the presence of a weak single-ion anisotropy D>0, and explicitly demonstrate the presence of crossover phenomena in domain growth kinetics. At early times the dynamical exponent and the correlation function are governed by the isotropic zero-temperature fixed point. Beyond a crossover time t_c(D), the dynamics is controlled by the Ising zero-temperature fixed point. Thus D is relevant at the isotropic zero-temperature fixed point. Using a renormalization group analysis around the isotropic zero-temperature fixed point we determine the value of the crossover exponent Φ.