  In this work, we explore the critical behaviors of fidelity susceptibility
and trace distance susceptibility associated to the steady states of
dissipative systems at continuous phase transitions. We investigate on two
typical models, one is the dissipative spin-1/2 XYZ model on two-dimensional
square lattice and the other is a driven-dissipative Kerr oscillator. We find
that the susceptibilities of fidelity and trace distance exhabit singular
behaviors near the critical points of phase transitions in both models. The
critical points, in thermodynamic limit, extracted from the scalings of the
critical controlling parameters to the system size or nonlinearity agree well
with the existed results.
