The Ising Model Essay Example | Topics and Well Written Essays - 1500 words

The Ising Model - Essay Example Although the Ising Model has been named after E. Ising, the inventor of the Model is W. Lenz. Lenz gave this model as a problem to solve to his disciple Ising. In Beitrà ¤ge zum Verstà ¤ndnis der magnetischen Eigenschaften in festen Kà ¶rpern, Lenz (1920) put forward the idea of a systematic physical-statistical model to comprehend the magnetic properties in solids. A few years later, in Beitrag Zur Theorie des Ferromagnetismus, Ising (1925) solved the Ising Model in one dimension which has no phase transition. In explaining the Model, Cipra (1987) focuses on the formation of binary alloys and the process of ferromagnetism with special reference to spontaneous magnetization as the original application areas of the work of Ising (1925). â€Å"The latter is also of interest historically: an understanding of ferromagnetism – and especially â€Å"spontaneous magnetization† – was the original purpose of the Ising model and the subject of Ising’s doctoral di ssertation.† (Cipra, 1985, p. 937) Generally, because of this historical importance, ferromagnetism is widely used to interpret and explain the various characteristics of the Ising Model.                  After Ising solved the Model in one dimension, no significant achievement could be made in the following years. However, much later in the year 1944, L. Onsager managed to solve the square lattice variety of Ising Model in two-dimensions through an analytical description. In the context of crystal statistics, Onsager (1944) described the phenomenon of phase change as â€Å"an order-disorder transition† (Onsager, 1944, p. 117). Almost a decade later, Yang (1952) explained spontaneous magnetization with the help of two-dimensional Ising Model. In this way, the study of higher dimensional varieties of Ising Model became feasible and the scope of the Model expanded beyond the realm of statistical physics. The Model was extensively used to study the inter-particle interactions to understand the behaviors of atoms and molecules of the real substance in the course of phase transitions. (Brush, 1967)