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

We propose a generalization of the coherent anomaly method to extract critical exponents phase transition occurring in steady-state 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 scaling properties singularity response functions determined through cluster mean-field calculations. apply this dissipative transverse-field Ising model and XYZ two dimensions obtaining convergent results already with small clusters.