A CLUSTER MODEL OF QUASI-ONE-DIMENSIONAL H(D)-ORDERING PHASE-TRANSITIONS

Basing on the previous study on Isotope effect in hydrogen bonded crystals, the equation for the critical temperature T(c) is presented in a cluster approximation. The obtained T(c) includes the information of hydrogen bond lengths (oxygen-oxygen distance R(O-O), hydrogen-hydrogen distance R(H-H) etc.), and has an extended form of that in pseudo-spin model which gives the exact solution in the one-dimensional hydrogen bonded systems. From theoretical viewpoint, experimental data of T(c)-R(O-O) and T(c)-R(H-H) relations are analyzed. It is pointed out that the quantum effect of H(D) atoms leads to the isotope effect in these geometric values, but this isotope effect contributes to T(c) in a quite different manner depending on R(O-O).