Random-field smearing of the proton-glass transition

Within a replica-symmetric mean-field theory we have studied the proton pseudo-spin-glass behavior of a random-bond classical Ising system in a homogeneous transverse field and a random longitudinal field. This model is expected to describe some properties of the mixed hydrogen-bonded ferro- and antiferroelectric crystals such as Rb₁-ₗ (NH₄) ₗH₂PO₄ which have recently been investigated experimentally. It is shown that in the presence of Gaussian random fields with zero mean and variance the proton-glass transition is smeared out, i. e. , the cusp in the dielectric susceptibility is rounded off and the proton-glass order parameter remains finite at temperatures above the nominal freezing temperature. However, the average dielectric polarization is strictly zero for a symmetric bond distribution. We have also determined the limits of stability of the replica-symmetric solution for the case of a deuterated system (=0). The replica-symmetric proton-glass phase is separated from the phase with broken replica symmetry by a line of instability in the (T, ) plane. The crossing of this line is thus connected with a phase transition which persists in the presence of random fields. Finally, the distribution function of local parallel fields P (h) determining the magnetic resonance line shape has been calculated within the random-field model and the results applied to interpret some recent experimental data.