Tunneling model of proton glasses

Abstract

The static critical behavior of a mixed hydrogen-bonded ferro-antiferroelectric system is investigated with use of a pseudo-spin Ising model in a transverse field, which describes the tunneling of protons. Assuming an infinite-ranged random interbond coupling, then→0 replica method is applied to evaluate the averaged free energy, from which the replica-symmetric solution of the Sherrington-Kirkpatrick type is obtained. It is shown that a proton pseudo-spin glass (PG) phase exists below a freezing temperatureT _f , whereT _f and the order parameters for the PG and ferroelectric phase are parametrized by the tunneling frequency Ω. For Ω ≧ Ω_c, where Ω_c =$\tilde J$ and$\tilde J$ is the random distribution width, no ordering is possible even forT→0. Numerical solutions for the PG order parameter and the dielectric susceptibility atT≠0 are obtained, and the phase diagram for a simple model of a mixed system atT→0 is presented.