Introduction to the Ising Model

Several transformations are used to reduce more complex Ising models on two-dimensional lattices to known exact solutions. As such, this compilation discusses systems based on the standard square lattice, the more elaborate 4-6 lattice and the triangular lattice. Four examples of solvable models are studied that include pairwise and multiple sites interactions with nearest neighbours. The authors develop a number of models that describe the cooperative binding of ligand molecules to a DNA polymer using an approach based on the one-dimensional Ising model The binding of ligands on a two-dimensional microarray matrix requires the development of a two-dimensional Ising model to describe cooperative interactions between bound ligand molecules. In the penultimate study, the magnetic and electronic properties of LiVOPO4, VOPO4, LiFePO4 and FePO4 compound cathodes are studied using Ab initio calculations, high temperature series expansions calculations and Monte Carlo simulations. In the closing chapter, the authors comprehensively examine a pseudo-critical behavior of the spin-1/2 Ising diamond and tetrahedral chains through a detailed examination of basic magnetothermodynamic quantities such as entropy, specific heat and susceptibility.