  We analyze the scaling parameter, extracted from the fidelity for two
different ground states, for the one-dimensional quantum Ising model in a
transverse field near the critical point. It is found that, in the
thermodynamic limit, the scaling parameter is singular, and the derivative of
its logarithmic function with respect to the transverse field strength is
logarithmically divergent at the critical point. The scaling behavior is
confirmed numerically by performing a finite size scaling analysis for systems
of different sizes, consistent with the conformal invariance at the critical
point. This allows us to extract the correlation length critical exponent,
which turns out to be universal in the sense that the correlation length
critical exponent does not depend on either the anisotropic parameter or the
transverse field strength.
