Growth Law and Superuniversality in the Coarsening of Disordered Ferromagnets

Abstract

We present comprehensive numerical results for domain growth in the two-dimensional {\it Random Bond Ising Model} (RBIM) with nonconserved Glauber kinetics. We characterize the evolution via the {\it domain growth law}, and two-time quantities like the {\it autocorrelation function} and {\it autoresponse function}. Our results clearly establish that the growth law shows a crossover from a pre-asymptotic regime with "power-law growth with a disorder-dependent exponent" to an asymptotic regime with "logarithmic growth". We compare this behavior with previous results on one-dimensional disordered systems and we propose a unifying picture in a renormalization group framework. We also study the corresponding crossover in the scaling functions for the two-time quantities. Super-universality is found not to hold. Clear evidence supporting the dimensionality dependence of the scaling exponent of the autoresponse function is obtained.

Thoroughly revised manuscript. The Introduction, Section 2 and Section 4 have been largely rewritten. References added. Final version accepted for publication on Journal of Statistical Mechanics: Theory and Experiment

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• Aging processes in systems with anomalous slow dynamics
• Ageing at the Spin-Glass/Ferromagnet Transition: Monte Carlo Simulation using GPUs
• Dynamic fluctuations in unfrustrated systems: random walks, scalar fields and the Kosterlitz-Thouless phase
• Topological regulation of activation barriers on fractal substrates
• Phase ordering in disordered and inhomogeneous systems
• Relaxation processes in a system with logarithmic growth