Effect of tunnelling and glass phase in mixed crystals of KDP type

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Abstract
Some thermodynamical and dynamical properties of mixed ferro- and antiferroelectric crystals with hydrogen bonds of the KDP type are investigated theoretically in the framework of the transversal Ising model with random competing interactions where the transverse field describes the tunnelling of the protons. The phase diagram derived for this model suggests the existence of a proton glass phase. The strength of the tunnelling Ω0 c is found to be important for the character of the dynamics of the model. There exists a lower critical tunnelling constant Ω0 c such that for Ω < Ω0 c the system behaves nonergodically at arbitrary temperatures. For Ω > Ω0 c a nonergodic behaviour is possible only for T < Tf . For certain values of the tunnelling constant Ω the temperature Tf agrees with the transition temperature to the proton glass phase.