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We study the reduced fidelity susceptibility $\chi_{r}$ for an $M$-bodysubsystem of an $N$-body Lipkin-Meshkov-Glick model with $\tau=M/N$ fixed. Thereduced fidelity susceptibility can be viewed as the response of subsystem to acertain parameter. In noncritical region, the inner correlation of the systemis weak, and $\chi_{r}$ behaves similar with the global fidelity susceptibility$\chi_{g}$, the ratio $\eta=\chi_{r}/\chi_{g}$ depends on $\tau$ but not $N$.However, at the critical point, the inner correlation tends to be divergent,then we find $\chi_{r}$ approaches $\chi_{g}$ with the increasing the $N$, and$\eta=1$ in the thermodynamic limit. The analytical predictions are perfectagreement with the numerical results.

Many-body reduced fidelity susceptibility in Lipkin-Meshkov-Glick model