Abstract
We revisit the effects of short-ranged random quenched disorder on the universal scaling properties of the classical $N$-vector model with cubic anisotropy. We set up the nonconserved relaxational dynamics of the model, and study the universal dynamic scaling near the second order phase transition. We extract the critical exponents and the dynamic exponent in a one-loop dynamic renormalisation group calculation with short-ranged isotropic disorder. We show that the dynamics near a critical point is generically slower when the quenched disorder is relevant than when it is not, independent of whether the pure model is isotropic or cubic anisotropic. We demonstrate the surprising thresholdless instability of the associated universality class due to perturbations from rotational invariance breaking quenched disorder-order parameter coupling, indicating breakdown of dynamic scaling. We speculate that this may imply a novel first order transition in the model, induced by a symmetry-breaking disorder.
Highlights
The large-scale, macroscopic effects of disorder in statistical models and related condensed matter systems have been active fields of theoretical research for a long time
The principal results from this work are as follows. (i) We show that when the disorder is relevant, i.e., with N < 4, the dynamics near the second-order transition is generically slower than that in the pure model: We find that the dynamic exponent z = 2 + O( ), making it larger than its value in the corresponding pure model where z = 2 + O( 2) [13] for small
We have studied the nonconserved relaxational dynamics of the classical N-vector model with cubic anisotropy in the presence of quenched disorder
Summary
The large-scale, macroscopic effects of disorder in statistical models and related condensed matter systems have been active fields of theoretical research for a long time . (ii) We. show that quenched disorder with rotational symmetry breaking couplings between the disorder and the order parameter are relevant perturbations on the RG fixed points, with the RG flow trajectories running off to infinity, making the universality class of the model with isotropic disorder - order parameter coupling unobservable. Show that quenched disorder with rotational symmetry breaking couplings between the disorder and the order parameter are relevant perturbations on the RG fixed points, with the RG flow trajectories running off to infinity, making the universality class of the model with isotropic disorder - order parameter coupling unobservable This is generally true whether the corresponding pure model is isotropic or cubic anisotropic. That both nonzero v and D > 0 imply that the rotational invariance in the order parameter space is manifestly broken
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