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

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

van der Heiden, Luka (TU Delft Applied Sciences; TU Delft Electrical Engineering, Mathematics and Computer Science)

Pulvirenti, E. (mentor)
Thijssen, J.M. (mentor)
Dubbeldam, J.L.A. (graduation committee)
Chepiga, N. (graduation committee)

Delft University of Technology

Applied Mathematics

2022-11-15

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.

curie-weiss model
Gaussian
Spin lattice

http://resolver.tudelft.nl/uuid:0787bab2-80d7-4ed0-8f67-f422b5f00d40

Student theses

bachelor thesis

© 2022 Luka van der Heiden