Critical exponents of the random-field O(N) model

We calculate critical exponents of the random-field O(N) model with functional (4+ɛ)-expansion. The critical behavior of the random-field ferromagnet has been a puzzle for a long time. Past works predicted the critical exponents of the random-field ferromagnet in D dimensions to be the same as in the pure (D-2)-dimensional ferromagnet with the same number of the magnetization components. This result contradicts the experiments and simulations. We find the exponents different from those of the pure ferromagnet in (2+ɛ) dimensions. In contrast to previous approaches we take into account an infinite set of relevant operators emerging in the problem. We demonstrate how these previously missed relevant operators lead to the breakdown of the (6-ɛ)-expansion for the random-field Ising model. [1] D.E. Feldman, Int. J. Mod. Phys. B 22, 2945 (2001). [2] D.E. Feldman, e-print cond-mat/0010012.