  We study the critical properties of the Lipkin-Meshkov-Glick Model in terms
of the fidelity susceptibility. By using the Holstein-Primakoff transformation,
we obtain explicitly the critical exponent of the fidelity susceptibility
around the second-order quantum phase transition point. Our results provide a
rare analytical case for the fidelity susceptibility in describing the
universality class in quantum critical behavior. The different critical
exponents in two phases are non-trivial results, indicating the fidelity
susceptibility is not always extensive.
