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Journal of Physics A Mathematical and General

Short-time dynamics of first-order phase transition in a disordered system

Guangping Zheng

Published Nov 27, 2002• 3 citations
Publisher

Abstract

Nonequilibrium short-time dynamics of first-order phase transition in a driven-disordered system at zero temperature is investigated. In a random-bond Ising model under external field, the largest discontinuous jump of order parameter shows a power-law evolution in short times: Δ M ( t ) ∼ t θ . The scaling exponent θ is equal to ( d − β/ν)/ z , where d is the dimensionality; β, ν and z are the critical exponents of the system. θ is found to be a universal exponent for any metastable relaxation in the short-time regime. This investigation suggests that the short-time dynamics is valid for the first-order phase transition in the driven disordered system and the critical phenomenon of the disordered system can be understood in the framework of nonequilibrium dynamics.

DOI
10.1088/0305-4470/35/49/305

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Dynamic scaling for driven disordered systems is investigated in some disordered Ising models. Using Monte Carlo simulation, we find that avalanches in both random-field and random-bond Ising models follow dynamic power-law scaling in short times, and the scaling relations are universal for the systems studied. The probability distribution of the dynamic scaling exponent theta is found to have two peaks centered at theta(1) and theta(2). The short-time dynamic exponent theta(1) is invariant and universal for all avalanches while the exponent theta(2) depends on the strength of disorder. The analytical result for the early stage evolution of breakdown process in the random-field Ising model is obtained using mean-field approximation. Short-time dynamic scaling is also confirmed.
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Dynamic scaling for fracture or breakdown process in disordered systems is investigated in a two-dimensional random field Ising model (RFIM). We find two evolving stages in the avalanche process in the RFIM. At the short-time regime, a power-law growth of the avalanche size Deltas is observed; and at late times, the conventional nucleation and growth process is found. At the critical point of the RFIM, the avalanche size is found to obey the dynamic scaling law Delta(s) approximately equal t((d-beta/nu)/z). From this dynamic scaling relation, the critical strength of the random field D(c) and the critical exponents, beta, nu, and z, are determined. The observed dynamics is explained by a simple nucleation theory of first-order phase transformations.
Critical short-time dynamics in a bond-diluted Ising model is investigated in this paper using numerical simulations. The effective static and dynamic critical exponents determined by the power-law scaling are found to depend strongly on bond concentration and initial state. For weak disorder, the short-time scaling relations for the system quenched from high temperature are observed to hold. In the strong dilution limit, multiscaling relations for the system starting from the ordered state are found. Corrections to the short-time scaling are proposed. The effect of disorder on critical short-time dynamics is discussed.