  The behavior of the ground-state fidelity susceptibility in the vicinity of a
quantum critical point is investigated. We derive scaling relations describing
its singular behavior in the quantum critical regime. Unlike it has been found
in previous studies, these relations are solely expressed in terms of
conventional critical exponents. We also describe in detail a quantum Monte
Carlo scheme that allows for the evaluation of the fidelity susceptibility for
a large class of many-body systems and apply it in the study of the quantum
phase transition for the transverse-field Ising model on the square lattice.
Finite size analysis applied to the so obtained numerical results confirm the
validity of our scaling relations. Furthermore, we analyze the properties of a
closely related quantity, the ground-state energy's second derivative, that can
be numerically evaluated in a particularly efficient way. The usefulness of
both quantities as alternative indicators of quantum criticality is examined.
