The glass transition and the replica symmetry breaking in vortex matter

We quantitatively describe the competition between the thermal fluctuations and the disorder using the Ginzburg -- Landau approach. Flux line lattice in type II superconductors undergoes a transition into three "disordered" phases: vortex liquid (not pinned), homogeneous vortex glass (pinned) and crystalline Bragg glass (pinned) due to both thermal fluctuations and random quenched disorder. We show that disordered Ginzburg -- Landau model (valid not very far from H_{c2}) in which only the coefficient of a term quadratic in order parameter psi is random first considered by Dorsey, Fisher and Huang leads to a state with nonzero Edwards -- Anderson order parameter, but this state is still replica symmetric. However when the coefficient of the quartic term psi^4 in GL free energy also has a random component, replica symmetry breaking effects appear. The location of the glass transition line in 3D materials is determined and compared to experiments. The line is clearly different from both the melting line and the second peak line describing the translational and rotational symmetry breaking at high and low temperatures respectively. The phase diagram is therefore separated by two lines into four phases mentioned above.