An Introduction to the Ising Model


Samuli Luoma (Editor)

Series: Mathematics Research Developments
BISAC: MAT029000

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. (Imprint: Novinka)

Table of Contents

Table of Contents


Chapter 1. Exact Results for Two-Dimensional Ising Models Obtained by Transformation Methods
(Viktor Urumov, Faculty of Natural Sciences and Mathematics, Saints Cyril and Methodius University, Skopje, Macedonia)

Chapter 2. Cooperative Interactions between Ligand Molecules in Microarray Hybridization
(Yury D. Nechipurenko, Engelhardt Institute of Molecular Biology, Russian Academy of Sciences, Moscow, Russia)

Chapter 3. Magnetic and Electronic Properties of LiXPO4 (X=VO and Fe) Cathode Materials
(R. Masrour, A .Jabar, E. K. Hlil, S. Obbade, C. Rossignol and Y. Boughaleb, Faculty of Science, Laboratory of Solid State Physics, Sidi Mohammed Ben Abdellah University, Dhar Mahraz, Fez, Morocco, and others)

Chapter 4. Pseudo-Critical Behavior of Spin-1/2 Ising Diamond and Tetrahedral Chains
(Jozef Strecka, Faculty of Science, Department of Theoretical Physics and Astrophysics, P. J. Safarik University, Kosice, Slovak Republic)


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