Simple Models for Complex Relaxation
The nonexponential relaxation of spin glasses, and other complex physical system can be interpreted within two different paradigms. In the ‘parallel’ approach, one assumes the existence of ‘effectively’ independent entities, i.e. clusters or droplets as for instance in Refs. [1,2]. Each of these is characterized by a relaxation time, which can be temperature and age dependent. The nonexponential relaxation follows then from a superposition of independent relaxation processes. Alternatively, one might think of the system as a highly correlated entity, and of relaxation as a series of steps which are subordinate to each other, which is the hierarchical approach. Experimental evidence in support of one picture rather then the other would require detailed information on microscopic correlations, which is so far not available. Even in numerical simulations, the existence of the basic objects of both approaches, has not been conclusively demonstrated. In this situation most theoretical descriptions are highly parametrized and experimentally hard to check. One may then ask how few assumptions one needs to reproduce the experimental data. In this paper we describe an attempt in this direction, i.e. a description of relaxation of spin glass systems at the level of a master equation.
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