Abstract
A simple model of strongly disordered systems composed of anharmonic oscillators with quenched random interactions is introduced and its structural phase transition is studied by making use of the replica method. A freeze-in transition characterized by Edwards and Anderson type's order parameter (q *0), the phase diagram (para-ferrodistortive-frozen), and a constant susceptibility below the transition temperature are derived in the mean field (Einstein oscillator) approximation. The self-consistent phonon approximation is also used to study the effect of spatial fluctuations, and it is shown that the phase diagram undergoes a qualitative change at the spatial dimension d=4. The relationship between our model and the Ginzburg-Landau theory of spin.glasses are discussed.
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