Vertex models for the antiferroelectric transition in squaric acid

Publisher Website
Google Scholar
Abstract
We consider two‐dimensional 4‐ and 12‐vertex models on a square lattice for the phase transition in the layered hydrogen‐bonded antiferroelectric crystals H2C4O4 and its deuterated isomorph. An exact solution for the 4‐vertex model, which strictly obeys the ’’ice‐rules’’, leads to a vanishing free‐energy. The 12‐vertex model, which takes into account the single ionized configurations, gives a second order phase transition in the framework of the Bethe approximation. The high‐temperature entropy of the 12‐vertex model is calculated exactly and agrees with the value predicted by the Bethe approximation. An exact calculation of the partition function for a modified 12‐vertex model, with a more degenerate ground state, leads to a well behaved thermodynamic potential. Also, we add a mean‐field interlayer interaction to the 12‐vertex model for predicting the correct low‐temperature ordering in squaric acid. Some thermodynamic quantities are explicitly calculated for this model.