Generalized Ferroelectric Model on a Square Lattice

A completely general square‐lattice ferroelectric model is considered, in which the configuration energies have arbitrary values at each vertex. It is found that the partition function can be evaluated by straightforward extensions of the method used for the regular ice, F‐ and KDP‐models, provided three sets of conditions are satisfied. These ensure that the two ordered F‐model states are degenerate (in the limit of a large lattice), so we conclude that the application of any staggered field which breaks this degeneracy also renders the problem insoluble by the present methods. The partition function for these ordered states is obtained explicitly and found to be given quite simply as a product of certain parameters associated with each vertex. Finally some conjectures are made concerning the spontaneous staggered polarization.