  In this paper we investigate the universality and scaling properties of the
well-known quantities in classical statistical mechanics near the quantum phase
transition point. We show that transverse susceptibility and derivatives of
correlation functions with respect to the parameter that drives the quantum
phase transitions, exhibit logarithmic divergence and finite size scaling the
same as entanglement. In other words the non-analytic and finite size scaling
behaviors of entanglement is not its intrinsic properties and inherit from the
non-analytic and scaling behaviors of correlation functions and surveying at
least the nearest neighbor correlation functions could specify the scaling and
divergence properties of entanglement. However we show that the correlation
functions could capture the quantum critical point without pre-assumed order
parameters even for the cases where the two-body entanglement is absent.
