Pseudo equilibrium description of disordered systems
We discussed the pseudo equilibrium description of quenched random systems. By generalizing the grand canonical ensemble it was possible to take into account frozen in spatial distributions of atoms on a lattice. The difference to the grand canonical ensemble for annealed systems is given by additional chemical potentials or forces of constraints, which are conjugated to the momenta of the occupation numbers. The obtained description is completely equivalent to the conventional description, based on the configurational average of the free energy. However, the construction of a partition function or generating functional allows to apply successful methods, which have been developed for equilibrium systems, to treat quenched disordered systems. The experience from field theoretical investigations of random ferromagnets13, which are briefly discussed in a second article in this volume14, seems to indicate that the pseudo equilibrium description of disordered systems may be applied also for further problems as for instance the localization phenomena.
Although this method has been discovered3 and rediscovered15 to perform concrete calculations, it has been considered also for more general investigations to understand the difference between annealed and quenched systems 5. Because the forces of constraints delivers a quantitative information upon the interaction of the spins with the occupation numbers, it was possible to check to validity of an ideal quenched model. Obviously, diverging spin energy fluctuations show that the assumption of ideal quenching may be rather unphysical.
KeywordsPartition Function Occupation Number Thermodynamical Potential Grand Canonical Ensemble Random System
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