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

References in corpus (7)

• Ageing in disordered magnets and local scale-invariance
• Growing correlations and aging of an elastic line in a random potential
• Superuniversality in phase-ordering disordered ferromagnets
• Scaling and super-universality in the coarsening dynamics of the 3d random field Ising model
• Aging in coarsening diluted ferromagnets
• Generic features of the fluctuation dissipation relation in coarsening systems
• Reply to "Comment on 'Scaling of the linear response in simple ageing systems without disorder' "

Cited by in corpus (15)

• Crossover in Growth Law and Violation of Superuniversality in the Random Field Ising Model
• Coarsening and percolation in a disordered ferromagnet
• Ageing at the Spin-Glass/Ferromagnet Transition: Monte Carlo Simulation using GPUs
• Aging processes in systems with anomalous slow dynamics
• Ordering Kinetics in the Random Bond XY Model
• Dynamic fluctuations in unfrustrated systems: random walks, scalar fields and the Kosterlitz-Thouless phase
• Ordering Dynamics of the Random Field Long-range Ising Model in One Dimension
• Domain Growth and Aging in the Random Field XY Model: A Monte Carlo Study
• Topological regulation of activation barriers on fractal substrates
• Phase ordering in disordered and inhomogeneous systems
• Relaxation processes in a system with logarithmic growth
• Equilibrium structure and off-equilibrium kinetics of a magnet with tunable frustration
• Effects of Frustration on Fluctuation-dissipation Relations
• Ordering kinetics in q-state random-bond clock model: Role of Vortices and Interfaces
• Domain Growth in Long-range Ising Models with Disorder