The Ising Ladder: Structure and Application to Ising Model on a Square Lattice.
Cluster methods have been important over the years for the understanding of infinite many body system; from mean field theory to the Bethe approximation ... In this thesis we make a special choice of cluster running throughout our chosen system: An infinite two dimensional lattice. The clusters so chosen are the Isotropic ladder and the anisotropic ladder. For these ladders, we are able to exhibit the free energy, which as usual is considered as the generator of "everything". The usual mean field method consists of dressing the cluster with mean fields. Instead we use a novel effective field approximation applied to the isotropic ladder to determine the critical temperature. In this way we recover the exact Onsager critical temperature for a two dimensional Ising model. In another approach we use the anisotropic ladder and besides obtaining the free energy we show how by the use of two self consistent relation, the critical temperature could be determined.
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- Statistics; Physics: Condensed Matter; Physics: Fluid and Plasma