Finite block pseudo-spin approach of proton glass

• The proton glass phase in hydrogen-bonded crystals.
• Ordering between block pseudo-spins comprised of random pseudo-spins.
• Dielectric susceptibility for the approximations of the Brillouin function.
• The freezing temperature of glass transition in Rb1−x(NH4)xH2PO4.

We herein propose an alternative phenomenology to explain the phase of proton glass by reference to finite block spin theory in magnetism, in which the phase may be considered as being a short-range ferroelectric ordering of block pseudo-spins comprised of random pseudo-spins that have a majority of individual pseudo-spins in a given sense. By making use of the Curie law of block pseudo-spins, we obtained the dielectric susceptibility for the lower and higher temperature approximations of the Brillouin function. The experimental results for the susceptibility in hydrogen-bonded mixed crystals of ferroelectric RbH2P(As)O4 and antiferroelectric NH4H2P(As)O4 were thus fitted fairly well at low temperatures in the proton glass phase whereas some deviation from our formulation was seen at high temperatures in the paraelectric phase.