  We study critical behaviors of the reduced fidelity susceptibility for two
neighboring sites in the one-dimensional transverse field Ising model. It is
found that the divergent behaviors of the susceptibility take the form of
square of logarithm, in contrast with the global ground-state fidelity
susceptibility which is power divergence. In order to perform a scaling
analysis, we take the square root of the susceptibility and determine the
scaling exponent analytically and the result is further confirmed by numerical
calculations.
