  The mean-field theory tells that the classical critical exponent of
susceptibility is the twice of that of magnetization. However, the linear
response theory based on the Vlasov equation, which is naturally introduced by
the mean-field nature, makes the former exponent half of the latter for
families of quasistationary states having second order phase transitions in the
Hamiltonian mean-field model and its variances. We clarify that this strange
exponent is due to existence of Casimir invariants which trap the system in a
quasistationary state for a time scale diverging with the system size. The
theoretical prediction is numerically confirmed by $N$-body simulations for the
equilibrium states and a family of quasistationary states.
