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 $6-ε$ 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 non-trivial fixed point in $6-ε$ dimensions is stable, contrary to the argument by Brézin and De Dominicis. We also computed the exponents $ν$ and $η$ by the $ε$ expansion. The results are consistent with the argument of the dimensional reduction at least in the leading order.