  We propose a mechanism to induce negative AC permittivity in the vicinity of
a ferroelectric phase transition involved with spontaneous symmetry breaking.
This mechanism makes use of responses at low frequency, yielding a high gain
and a large phase delay, when the system jumps over the free-energy barrier
with the aid of external fields. We illustrate the mechanism by analytically
studying spin models with the Glauber-typed dynamics under periodic
perturbations. Then, we show that the scenario is supported by numerical
simulations of mean-field as well as two-dimensional spin systems.
