Long-range correlated random magnetic fields in the nonlinearσmodel

The effect of the long-range correlated random magnetic fields which behave like $〈h(x)h(y)〉$ ~1|x-y|^d-σ on the critical phenomena is discussed with the use of the nonlinear σ model. The crossover between the two critical behaviors dominated by the long-range and short-range disorder fixed points is shown to occur at (m-2)σ-d+4=0 (m is the spin dimensionality). The critical exponents calculated at the long-range disorder fixed point around the lower critical dimensionality 4+σ are not the same as those in d-2 expansions in the pure system.