THERMODYNAMICS OF THE ONE-DIMENSIONAL 6-VERTEX FERROELECTRIC MODEL WITH PROTON TUNNELING

We study a one-dimensional model of ferroelectrics with proton tunneli ng on the hydrogen bonds. The influence of tunneling on the thermodyna mics of the model is considered in the approximation of Nagle [exp(-w/ T) = 0] and for energies of the forbidden configurations w much larger than the tunneling constant GAMMA. The rearrangement of the energy le vels due to the inclusion of proton tunneling is investigated by secul ar perturbation theory, using GAMMA/w as a small parameter. Exactly so lvable six-vertex one-dimensional models with tunneling are obtained a s the first nonvanishing orders of this theory. The phase transition f rom the disordered to the polar phase is found to be first order as in the case of GAMMA = 0, but the transition temperature T(c) and the en tropy jump DELTAS decrease with the increase of the parameter delta = GAMMA2/epsilonw, where epsilon is the energy of the excited configurat ions obeying the ice rule. When gamma = (1 - delta) --> 0, T(c), DELTA S, and the energy gap, separating the ground ferroelectric state from the excited states, tend to zero as 2epsilon/ln(1/gamma), (gamma/2)ln( 1/gamma), and epsilongamma, respectively. The results are compared wit h the experimental data on the ferroelectric, K(HxD1-x)PO4.