Fluctuation effects in the Ising model with reduced interaction and quenched disorder

The effect of quenched random fields and local perturbations of critical temperature 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. Using the replica method the dimensional reduction by 2 for systems with finite-range interaction and quenched random fields 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.