The randomly dilute Curie-Weiss model with Gaussian, bounded and sub-Gaussian couplings

Bachelor thesis (2022)

Authors

L.M. van der Heiden Applied Sciences

Contributors

E. Pulvirenti Applied Probability (mentor)
J.M. Thijssen QN/Thijssen Group (mentor)
Johan L.A. Dubbeldam Mathematical Physics (graduation committee member)
Natalia Chepiga QN/Chepiga Lab (graduation committee member)
Faculty
Applied Sciences, Applied Sciences
Copyright: © 2022 Luka van der Heiden
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Published Date

15-11-2022

Language

English

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Faculty

Applied Sciences

Abstract

The behaviour of the dilute Curie-Weiss model has been analysed for Gaussian, bounded and subGaussian couplings. This model is an abstraction of the Curie-Weiss model which is a model of a spin configuration where instead of a constant coupling between spins the spin coupling is a realisation of a random variable. To analyse this behaviour first the behaviour of the standard Curie-Weiss model is depicted. A notable part from this behaviour is the presence of a phase transition., indicating that this model can be used for a study of phase transitions. After having analysed the behaviour of the standard Curie-Weiss model theorems, stating the closeness between the standard Curie-Weiss model and the randomly dilute Curie-Weiss model for Gaussian, bounded and sub-Gaussian couplings, will be proven. Indicating that the models behave approximately the same way. These theorems will be in the form of a bound for the on randomly dilute Curie-Weiss model as an exponential multiplied by the standard Curie-Weiss model with the probability of this bound being a sub-Gaussian distribution.

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