  Fisher information, lies at the heart of parameter estimation theory, was
recently found to have a close relation with multipartite entanglement
(Pezz\'{e} and Smerzi, Phys. Rev. Lett. 102, 100401). We use Fisher information
to distinguish and characterize behaviors of ground state of the
Lipkin-Meskhov-Glick model, which displays a second-order quantum phase
transition between the broken and symmetric phases. We find that the parameter
sensitivity of the system attains the Heisenberg limit in the broken phase,
while it is just around the shot-noise limit in the symmetric phase. Based on
parameter estimation, Fisher information provides us an approach to the quantum
phase transition.
