Exact solutions for Ising model correlations of the decorated-square lattice : [an honors thesis (HONRS 499)]/ Lisa Marie Pawlowski.

Abstract

This thesis project involved the study of exact solutions for magnetic spin correlations on a regular- and a decorated-square Ising lattice structure. Existent knowledge of correlations on a regular-square Ising structure is sufficient to determine exact correlation values on a select, spatially compact, decorated structure. These values can be represented as linear combinations of regular-square Ising spin correlation through the use of linear-algebra and the decoration-iteration transformation. Multispin localized correlations are studied over a broad range of temperatures and are found to decrease with increasing temperature. At very low temperatures, all correlation are found to saturate to unity regardless of spin separation and quantity of spins involved.