A soluble seven-vertex model for clusters with interfacial bending energy

Abstract

A model describing an ensemble of disjoint clusters on a square lattice is introduced. In addition to the usual surface energy terms, in x and in y, the model includes a bending energy in c per corner in the interface. It is formulated as a seven-vertex model which is in general not solvable. For beta in c=ln(2)/2, however, this seven-vertex model becomes free fermionic one and an exact expression for its free energy is derived. In the extreme anisotropic ('Hamiltonian') limit the operator content coincides with that of the 1D Ising model in a transverse field. Three critical lines with Ising-like behaviour are found.