Monte Carlo simulations with an effective Hamiltonian originally constructed for BaTiO$_3$ [1] are used to study the dielectric response of a ferroelectric system near a phase transition. Landau theory predicts for a continuous transition a linear dependence of the inverse susceptibility on temperature, and a definite relation (a factor of 2) between the slopes on both sides of the transition. For the cubic-tetragonal transition in BaTiO$_3$ (a weakly first-order transition), experiments and Monte Carlo simulation show that the slope ratio is significantly higher. While several alternative hypotheses have been put forward to account for this behavior, there are indications [2] that the slope ratio might be an increasing function of the order-disorder (Ising-like) character of the phase transition (being two only in the displacive limit). To explore this idea we have performed simulations in which the depth of the potential wells in the effective hamiltonian is altered to achieve varying degrees of order-disorder character (the deeper the well, the more Ising-like the Hamiltonian). The dielectric susceptibility is computed directly from the width of the statistical distribution of the ferroelectric mode variables in the Monte Carlo simulation.

References:
[1] W. Zhong, D. Vanderbilt and K. M. Rabe, Phys. Rev. Lett. 73, 1861 (1994); Phys. Rev. B52, 6301 (1995).
[2] S. Radescu, I. Etxebarria, and J.M. Perez-Mato, J. Phys.: Condens. Matter 7, 585 (1995).