Applications of the transfer integral techniques to two-dimensional lattices

The transfer integral formalism is used to study the statistical mechanical properties of a two-component field defined on a two-dimensional lattice. This field, taken to have anisotropic elasticity, is subject to both a nonlinear local potential and an external field. The free energy and magnetization are calculated using an approximate solution of the transfer integral problem. This solution employs a strong-coupling approximation to the transfer integral equation and a variational principle with correlated Gaussian trial functions. As a special case, the ø4 model for a structural phase transition, in the absence of an applied field, is analyzed; a phase diagram consistent with previous calculations is obtained. The phase diagram for a two-component field, with anisotropic elasticity, a ø4 local potential, and an external field, is also considered.