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 Ω and a random longitudinal field. This model is expected to describe some properties of the mixed hydrogen-bonded ferro- and antiferroelectric crystals such as ${\mathrm{Rb}}_{1\mathrm{-}\mathit{x}}$(${\mathrm{NH}}_4$ ${)}_{\mathit{x}}$ ${\mathrm{H}}_2$ ${\mathrm{PO}}_4$ which have recently been investigated experimentally. It is shown that in the presence of Gaussian random fields with zero mean and variance Δ 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 (Ω=0). The replica-symmetric proton-glass phase is separated from the phase with broken replica symmetry by a line of instability in the (T,Δ) 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.