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.

Author Bio

Eva graduated Villanova University in 2010 with a Bachelors of Science degree in Mathematics, and minors in Applied Physics and Theology. She did the work of this paper at St. Michael's College during the summer of 2008. She is looking forward to the opportunities of the future while teaching middle school and starting a small jewelry business. Outside of academics, Eva enjoys dancing Argentine Tango and folding origami.