Dissipative phase transition in two-dimensional d-wave Josephson junctions

Quantum dynamics of in-plane Josephson junctions between two d-wave superconducting films is described by the anisotropic XY-model where both, quasiparticle and Cooper pair tunneling terms, appear to be equally non-local. Applying a combination of the weak and strong coupling analyses to this model, we find a compelling evidence of a dissipative phase transition. The corresponding critical behavior is studied and contrasted with that found previously in the conventional (s-wave) Josephson junctions.