The scaling behavior of logarithmic fidelity in quantum phase transition   in LMG model
  In this paper, we explore the differences between classical logarithmic fidelity and quantum fidelity. The classical logarithmic fidelity is found to be always extensive while the quantum one manifests distinct size dependence in different phases. Illustrated by the anisotropic Lipkin-Meshkov-Glick model, we found numerically and analytically that the logarithmic fidelity scales like N in the symmetry-broken phase and scales like N^0 in the polarized phase. The singular behavior around the critical point is also investigated. 
Ching-Yee Leung, Ho-Man Kwok, Shi-Jian Gu, Hai-Qing Lin
cond-mat.stat-mech cond-mat.mes-hall quant-ph