We propose a pseudospin model for the Rb 1−x (NH 4 ) x H 2 PO 4 type proton glasses, which takes into account energy levels of hydrogens near a PO 4 group (within a cluster approximation), long-range interactions between the hydrogen bonds, and an internal random deformational field. Relaxation is explored within the framework of the Glauber dynamics. We obtain a qualitative description of temperature behavior of the state parameters and dielectric permittivities of Rb 1−x (ND 4 ) x D 2 PO 4 compounds at different frequencies.

For theoretical description of pseudospin systems with essential shortrange and long-range interactions we use the method based on calculations of the free energy functional taking into account the short-range interactions within the reference approach in cluster approximation. We propose a consistent formulation of the cluster expansion method for quantum pseudospin systems. We develop a method allowing one to obtain within the cluster approximation an Ornstein-Zernike type equation for reference cumulant Green function of an arbitrary order. In the two-particle cluster approximation we derived an explicit expression for pair temperature cumulant Green function of the reference system. In the cluster random phase approximation we calculated and studied thermodynamic characteristics, elementary excitation spectrum, and integral intensities of the Ising model in transverse field.

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We consider a spin-glass model with an arbitrary range of competing interactions within two-particle cluster approximation for the free energy and within symmetric replica approach. We show that for the thermodynamic characteristics, the Gaussian approximation for distribution functions of cluster (short-range) fields can be used. For a simple proton-glass model with weak long-range interactions (linear approximation) we study the influence of the long-range interactions and random internal fields on the phase diagram and thermodynamics characteristics. It is shown that small fluctuations of internal fields can lead to essential smearing of spin-glass transition region.