A nonlinear response theory is provided by use of the transient linearization
method in the spatially one-dimensional Vlasov systems. The theory inclusively
gives responses to external fields and to perturbations for initial stationary
states, and is applicable even to the critical point of a second order phase
transition. We apply the theory to the Hamiltonian mean-field model, a toy
model of a ferromagnetic body, and investigate the critical exponent associated
with the response to the external field at the critical point in particular.
The obtained critical exponent is nonclassical value 3/2, while the classical
value is 3. However, interestingly, one scaling relation holds with another
nonclassical critical exponent of susceptibility in the isolated Vlasov
systems. Validity of the theory is numerically confirmed by directly simulating
temporal evolutions of the Vlasov equation.Comment: 15 pages, 8 figures, accepted for publication in Phys. Rev. E, Lemma
2 is correcte
