Random-field effects in critical phenomena. Exactly solvable model

Abstract

The effect of quenched random fields on the critical behavior at phase transitions is studied within the framework of an exactly solvable model that takes into account interaction of fluctuations with equal and opposite momenta and belongs to the universality class of the spherical model. Using the replica method the dimensional reduction by 2 for systems with finite-range interaction is explicitly shown. For interaction of the infinite range the model demonstrates the mean field critical asymptotics independently of dimensionality or the presence of random fields.