Theory of the phase transition in the layered hydrogen-bonded SnCl2· 2H2O crystal

On the foundations established by previous experimental and theoretical investigations a basic model is constructed for the protonic order-disorder transition in Sn${\mathrm{Cl}}_2$ · 2${\mathrm{H}}_2$O. This model is comparable to the Slater model of K${\mathrm{H}}_2$P${\mathrm{O}}_4$ (KDP) in spirit, in degree of complexity, and in omission of refinements, although the two models are considerably different in detail. The basic model for Sn${\mathrm{Cl}}_2$ · 2${\mathrm{H}}_2$O is isomorphic to a planar dimer model and is solved exactly, including the pair-correlation functions which decay exponentially with distance except at the critical temperature. The exact solution requires a particular ground state for there to be a transition, and this ground state is the same as the one given by neutron diffraction. The exact solution also yields a highly symmetrical specific heat near $T_c$ which agrees with experiments, although the experiments indicate a stronger divergence ($\alpha =\frac{1}{2}={\alpha }^{\prime }$) than the logarithmically diverging specific heat predicted by the basic model. Several refinements of the basic model are proposed which should provide even better agreement with experiment.