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 the replica symmetry-breaking framework. It is found that, above the ferromagnetic transition temperature Tf, a glassy phase appears at intermediate temperatures Tf<T<Tb while the usual paramagnetic phase exists for TTb only. The correlation length at Tb is computed and found to be compatible with previous numerical results.