  Many-body systems when continuous phase transition occurs are mainly built in
the interrelationship between particles, implemented through many-body
correlations. Some of them may exhibit so-called topological order hardly
measured by experiments. Therefore we need, beyond mean-field theory, the
complex-systems approach that stresses the systemic complexity of many-body
network at criticality. According to our previous study, network space
experiences the homogeneous-heterogeneous transition invisible in traditional
phase transitions. The network robustness can be a useful indicator to capture
the critical phenomena of phase transitions with/without symmetry breaking. In
this work, we demonstrate the idea of the change of robust networks is
successfully applied to the well-known 1D quantum and 2D classical XY models.
