Critical Exponents of the Random-Field O(N) Model

The critical behavior of the random-field Ising model has long been a puzzle. Different methods predict that its critical exponents in D dimensions are the same as in the pure (D-2)-dimensional ferromagnet with the same number of the magnetization components contrary to the experiments and simulations. We calculate the exponents of the random-field O(N) model with the (4+ɛ)-expansion and obtain values different from the exponents of the pure ferromagnet in 2+ɛ dimensions. An infinite set of relevant operators missed in previous studies leads to a breakdown of the (6-ɛ)-expansion.