Renormalization group for the probability distribution of magnetic impurities in a random-field ${\varphi }^4$ model

Abstract

Extending the usual Ginzburg-Landau theory for the random-field Ising model, the possibility of dimensional reduction is reconsidered. A renormalization group for the probability distribution of magnetic impurities is applied. New parameters corresponding to the extra ${\varphi }^4$ coupling constants in the replica Hamiltonian are introduced. Although they do not affect the critical phenomena near the upper critical dimension, they can when dimensions are lowered.

16 pages, 11 figures, revtex

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