The Ising Model: Brief Introduction and Its Application

Abstract

Though the idea to use numerical techniques, in order to solve complex three-dimensional problems, has become quite old, computational techniques have gained immense importance in past few decades because of the advent of new generation fast and efficient computers and development of algorithms as parallel computing. Many mathematical problems have no exact solutions. Depending on the complexity of the equations, one needs to use approximate methods. But there are problems, which are beyond our limits, and need support of computers. Ernst Ising published his PhD dissertation in the form of a scientific report in 1925. He used a string of magnetic moments; spin up (+1/2) and spin down (À1/2), and applied periodic boundary conditions to prove that magnetic phase transition does not exist in one dimensions. Lars Onsager, latter, exactly solved the phase transition problem in two dimensions in 1944. It is going to be a century-old problem now. A variety of potential applications of Ising model are possible now a days; classified as Ising universality class models. It has now become possible to solve phase transition problems in complex three-dimensional geometries. Though the area of spinotronics still needs more engagements of computational techniques, its limited use have provided good insights at molecular scale in recent past. This chapter gives a brief introduction to Ising model and its applications, highlighting the developments in the field of magnetism relevant to the area of solid state physics.

A cooperative switch within the KaiC hexamer revealed by cryo-EM

“…We used an Ising model to describe correlations of the conformational states found within each hexamer [41][42][43] . This analysis reveals that there is substantial nearest-neighbor cooperativity in the ring with adjacent subunits tending to adopt the same conformation.…”

“…We find that these two states exist in a dynamic equilibrium because both states can be found in each mutant, suggesting that KaiA stimulates KaiC through a conformational selection mechanism. The buried state is much favored in the KaiC-EE mutant and we occasionally observed a distinct structure where the buried A-loop makes direct contacts with the 422-loop, previously implicated in the regulation of the phosphorylation reaction 40 .We used an Ising model to describe correlations of the conformational states found within each hexamer [41][42][43] . This analysis reveals that there is substantial nearest-…”

Traffic Intersection Lane Control Using Radio Frequency Identification and 5G Communication

“…The Potts and Ising models were adopted to determine the current status of the traffic lights at the intersection. The Potts model is an extension of the Ising model derived from statistical physics theory [13,15]. Both models refer to processes occurring in the structures of complex systems.…”

“…For the purpose of this paper, an application of models derived from the theory of statistical physics was used. The Ising model is primarily used for the analysis of phase changes [13][14][15]. Its initial application was in statistical mechanics and phase transitions in the magnetism model [16].…”

Potts Clustering with Complete Shrinkage: a novel clustering methodology with its Software Package pottscompleteshrinkage in Python

“…The Ising model is very famous as a model named after the physicist Ernst Ising: in 1925, Ernst who was a Lenz student, chose the model as the focus of his PhD dissertation (Kobe (2000), Kobe (1997), Ising (1925), Brush (1967), Ising et al (2017)). It is a NP-complete (Cipra, 2000) mathematical model of ferromagnetism in statistical mechanics ( Singh (2020), Giacomin & Mahfouf (2021), Cipra (1987), Glauber (1963), Pfeuty (1970), Brush (1967), Fredrickson & Andersen (1984), Stauffer et al (1993), Kadowaki & Nishimori (1998), Joya et al (2002), Aiyer et al (1990), Wen et al (2009), McCoy & Wu (2014)):…”