Critical exponents of the random-field O(N) model -: art. no. 177202

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 + epsilon) -expansion and obtain values different from the exponents of the pure ferromagnet in 2 + epsilon dimensions. An infinite set of relevant operators missed in previous studies leads to a breakdown of the (6 - epsilon) -expansion.