The 3-dimensional eight vertex model and the proton-proton correlation functions in ice

The transition temperature of the isotropic eight vertex model¹ (i.e. all vertices with 2 arrows have the same energy) is found to be the same for 2-or 3-dimensional (or more) lattices. The partition function of ice has the same diagrammatic expansion as the eight vertex model at the transition point (as already known³ in 2 dimensions). Therefore, the Fourier transform of the proton-proton correlation function in ordinary ice is expected to have a singularity at the origin, in agreement with approximate calculations.