Article

# Crossover in growth law and violation of superuniversality in the random-field Ising model.

Dipartimento di Fisica E. Caianiello and CNISM, Unità di Salerno, Università di Salerno, via Ponte don Melillo, 84084 Fisciano (SA), Italy.

Physical Review E (Impact Factor: 2.31). 02/2012; 85(2 Pt 1):021141. DOI: 10.1103/PhysRevE.85.021141 Source: PubMed

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**ABSTRACT:**We study numerically the phase-ordering kinetics of the two-dimensional site-diluted Ising model. The data can be interpreted in a framework motivated by renormalization-group concepts. Apart from the usual fixed point of the nondiluted system, there exist two disorder fixed points, characterized by logarithmic and power-law growth of the ordered domains. This structure gives rise to a rich scaling behavior, with an interesting crossover due to the competition between fixed points, and violation of superuniversality.Physical Review E 10/2013; 88(4-1):042129. · 2.31 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Recently, different numerical studies of coarsening in disordered systems have shown the existence of a crossover from an initial, transient, power-law domain growth to a slower, presumably logarithmic, growth. However, due to the very slow dynamics and the long-lasting transient regime, one is usually not able to fully enter the asymptotic regime when investigating the relaxation of these systems toward equilibrium. We here study two simple driven systems-the one-dimensional ABC model and a related domain model with simplified dynamics-that are known to exhibit anomalous slow relaxation where the asymptotic logarithmic growth regime is readily accessible. Studying two-times correlation and response functions, we focus on aging processes and dynamical scaling during logarithmic growth. Using the time-dependent growth length as the scaling variable, a simple aging picture emerges that is expected to also prevail in the asymptotic regime of disordered ferromagnets and spin glasses.Physical Review E 01/2013; 87(1-1):012114. · 2.31 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We consider the one-dimensional Glauber dynamics with coupling disorder in terms of bilinear fermion Hamiltonians. Dynamic exponents embodied in the spectrum gap of these latter are evaluated numerically by averaging over both binary and Gaussian disorder realizations. In the first case, these exponents are found to follow the nonuniversal values of those of plain dimerized chains. In the second situation their values are still nonuniversal and subdiffusive below a critical variance above which, however, the relaxation time is suggested to grow as a stretched exponential of the equilibrium correlation length.Physical Review E 06/2013; 87(6-1):062102. · 2.31 Impact Factor

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