Stability of a fixed point in the replica action for the random field Ising model

Abstract. We reconsider stability of the non-trivial fixed point in 6− ǫ dimensional effective action for the random field Ising model derived by Brézin and De Dominicis. After expansion parameters of physical observables are clarified, we find that the nontrivial fixed point in 6 − ǫ dimensions is stable, contrary to the argument by Brézin and De Dominicis. We also computed the exponents ν and η by the ǫ expansion. The results are consistent with the argument of the dimensional reduction at least in the leading order.