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Springer proceedings in physics

The 2d/3D Classical Heisenberg Ferromagnet

Robert Goodell Brown, Mikael Ciftan

Published Jan 1, 1993• 3 citations
Publisher
DOI
10.1007/978-3-642-78083-7_13

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The present thesis is focused on the study of the models of Ising and Heisenberg (classical) for ferromagnetism, the theory of phase transitions and the Monte Carlo method as an efficient computational scheme for dealing with these kinds of strongly interacting systems. With the aid of this method, computational simulations were performed for the above mentioned models in 2 and 3 dimensions (2D and 3D) in order to compare these results with the predictions of some theoretical models. The method followed to model these systems is indicated as well as the process for constructing phase diagrams for the main thermodynamic quantities of interest (mean magnetization, mean energy, specific heat, magnetic susceptibility) and their behavior in a vicinity of the critical point is analyzed. Furthermore, a quantitative analysis is carried out to calculate the corresponding critical exponents (_; _; and _) and to prove the phenomenon of universality they fulfill for different types of crystalline structure (3D case) and for the 2 models previously cited (Ising and Heisenberg). The programs written down in C++ that were constructed with the aim of performing the respective simulations are also included. \nKeywords: models of Ising and Heisenberg, ferromagnetism, phase transitions, Monte Carlo method, critical point, critical exponents, universality.