Glassy transition in the three-dimensional random field Ising model

The high temperature phase of the three dimensional random field Ising model is studied using replica symmetry breaking framework. It is found that, above the ferromagnetic transition temperature T_f, there appears a glassy phase at intermediate temperatures T_f<T<T_b while the usual paramagnetic phase exists for T>T_b only. Correlation length at T_b is computed and found to be compatible with previous numerical results.