Mean-field theory of the proton glass

The mixed ferroelectric-antiferroelectric compound (Rb${)}_{\mathit{x}}$(${\mathrm{NH}}_4$ ${)}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{H}}_2$ ${\mathrm{PO}}_4$ (RADP) exhibits a glassy phase which can be modeled as a spin glass. However, the protons whose order and disorder are being observed tunnel to a significant degree, making the spin glass an explicitly quantum-mechanical one. We solve the mean-field theory of a model for such a system, the Ising spin glass in a transverse field, by a novel combination of discretized-path-integral methods and replica techniques. The results provide an unambiguous microscopic picture of the effect of tunneling on a glass transition.