  We study dissipative phase transition near the critical point for a system
with two-photon driving and nonlinear dissipation. The proposed mean-field
theory, which explicitly takes into account quantum fluctuations, allowed us to
describe properly the evolution dynamics of the system and to demonstrate the
new effects in the steady-state. We show that the presence of quantum
fluctuations leads to a power-law dependence of the anomalous average at the
phase transition point, with which the critical exponent is associated. Also,
we investigate the effect of the quantum fluctuations on the critical point
renormalization and demonstrate the existence of a two-photon pump threshold.
It is noteworthy that the obtained results are in a good agreement with the
numerical simulations.
