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 ${\mathit{T}}_{\mathit{f}}$, a glassy phase appears at intermediate temperatures ${\mathit{T}}_{\mathit{f}}$<T<${\mathit{T}}_{\mathit{b}}$ while the usual paramagnetic phase exists for T≳${\mathit{T}}_{\mathit{b}}$ only. The correlation length at ${\mathit{T}}_{\mathit{b}}$ is computed and found to be compatible with previous numerical results.