Relaxational Processes in Frustrated Random Systems: A Spherical-Spin Model
A large variety of problems can be entered under the classification of random frustrated systems. The dynamical response of such systems appears to possess some universal characteristics, features common to systems very different in nature. Such features may be considered as being consequences of these two properties: of randomness, which implies that the system is characterised by a number of parameters that may be chosen from a set of values all of which are physically permitted, and of frustration, which implies that there are a set of constraints, not mutually compatible, that the system must satisfy in an optimal way. The prototypical examples of this kind of system are the much-studied spin glasses. Here the randomness and frustration enter in the magnetic interactions between spins. The sign and strength of the interaction between pair of spins can take on a number of different possible values, in a real spin glass. In consequence there arises a mutually incompatible set of rules that say, allow local but not global minimisation of the interaction energy. In a nonmagnetic context, alternatively, one may envisage polymers on a random substrate (Parisi, in this Workshop) which must satisfy connectivity constraints while trying to minimise local potential energy. The result is that, broadly speaking, the system finds a number of relatively satisfactory solutions to its problem of optimization, and the number of solutions grows extremely rapidly with the size of the system. The existence of multiple states of the system, associated with a spectrum of excitations of different energies, is what then gives rise to some characteristic time dependent properties.
KeywordsIsing Model Thermodynamic Limit Spin Glass Spin Correlation Spherical Constraint
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