Application of the transfer tensor method: A variational method

Abstract

We apply the transfer tensor method to get by a variational method approximated solutions of d-dimensional classical spin lattice models in statistical mechanics. We discuss the calculation of critical temperatures and also the limits, for which this variational method turns out to become exact. We apply this method to homogeneous and inhomogeneous Ising models. In the case of the 2-D random site model with nearest-neighbour interaction on a square lattice, the critical concentration x c is given by the solution of the equation x 2(2 x− x 2+2) = 1 being x c =0.593905…, which seems to be consistent with the best known numerical result, x c ≈0.593±0.002.