Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach

We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system. The method, originally developed by Suzuki [J. Phys. Soc. Jpn. {\bf 55}, 4205 (1986)] for equilibrium systems, is based on the scaling properties of the singularity in the response functions determined through cluster mean-field calculations. We apply this method to the dissipative transverse-field Ising model and the dissipative XYZ model in two dimensions obtaining convergent results already with small clusters.