This paper investigates the Ising model, a model conceived by Ernst Ising to model ferromagnetism. This paper presents a historical analysis of a model which brings together aspects of graph theory, statistical mechanics, and linear algebra. We will illustrate the model and calculate the probability of individual states in the one dimensional case. We will investigate the mathematical relationship between the energy and temperature of the model, and, using the partition function of the probability equation, show that there are no phase transitions in the one dimensional case. We endeavor to restate these proofs with greater clarity and explanation in order for them to be more accessible to other undergraduates.
Joanna Ellis-Monaghan, Department of Mathematics, Saint Michael's College firstname.lastname@example.org
"Phase Transitions in the Ising Model,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 11
, Article 10.
Available at: https://scholar.rose-hulman.edu/rhumj/vol11/iss2/10