Critical Behavior of the Pseudospin Model of Order-Disorder Type Ferroelectrics

Abstract

The behavior of the specific heat, the field-dependent susceptibility, and the soft mode is considered in the neighborhood of the critical point using the spin model for hydrogen-bonded ferroelectrics with a purely dipolar interaction. shape-independent results are obtained if one refers always to the state of zero internal field, i.e., with an external field present that just compensates the depolarizing field. The results are expressed in terms of the nonvanishing expectation values of single spin operators. These can be obtained either by solving self-consistency conditions or more crudely by using the molecular-field values. The critical co-efficients are given explicitly for the latter case. For the specific heat a logarithmic singularity is obtained, while the inverse susceptibility is found to depend linearly on $|T-T_c|$. The next higher-order response functions and the corresponding behavior of the soft mode, as well as the leading power in the electric field of the susceptibility and the soft mode at $T=T_c$, have also been calculated. The predicted critical behavior agrees with experimental results surprisingly close to the critical point.