We investigate response to an external magnetic field in the Hamiltonian
mean-field model, which is a paradigmatic toy model of a ferromagnetic body and
consists of plane rotators like the XY spins. Due to long-range interactions,
the external field drives the system to a long-lasting quasistationary state
before reaching thermal equilibrium, and the susceptibility tensor obtained in
the quasista- tionary state is predicted by a linear response theory based on
the Vlasov equation. For spatially homogeneous stable states, whose momentum
distributions are asymmetric with zero-means, the theory reveals that the
susceptibility tensor for an asymptotically constant external field is neither
symmetric nor diagonalizable, and the predicted states are not stationary
accordingly. Moreover, the tensor has no divergence even at the stability
threshold. These theoretical findings are confirmed by direct numerical
simulations of the Vlasov equation for the skew-normal distribution functions.Comment: 10 pages, 8 figure
