Phase transitions in disordered systems: Exactly solvable model

Abstract

The critical behavior at phase transitions of random systems is studied within the framework of an exactly solvable model which takes into account interactions of fluctuations with equal and opposite momenta. Using the replica method, the dimensional reduction by 2 for the φ4 model with a quenched random field is explicitly shown. Phase transitions in systems with two interacting order parameters which in addition are coupled to two independent random fields are also studied. In the absence of random fields the model demonstrates fluctuation induced phase transitions of the first order for spacial dimension d<4. In random systems with only one quenched random field present, second order phase transitions are restored. Two random fields suppress any phase transitions for d<4. For interaction of an infinite range, the model demonstrates the mean field critical asymptotics independently of dimensionality or the presence of random fields.