Phase transition of the low-dimensional tunnelling model

Abstract

The phase transition of the low-dimensional tunnelling model is investigated in a two-particle cluster approximation. By a perturbation expansion of the partition function the self-consistent equation for the effective field is obtained as a power series, and consequently the transition temperature and the susceptibility etc. are obtained in analytical forms. It is shown that the static properties largely depend upon the number of nearest neighbors, and that the one-dimensional model does not exhibit any transition. This approximation is also applied to the “pseudo” one-dimensional ferroelectrics like CsH₂PO₄ by taking account of the interaction between protons on different chains. It is found that the interchain correlations, even if they are weak, bring about the phase transitions with rather high transition temperatures. The antiferroelectric phase transition in this model is also discussed.