The randomly dilute Curie-Weiss model with Gaussian, bounded and sub-Gaussian couplings
L.M. van der Heiden (TU Delft - Applied Sciences)
Elena Pulvirenti – Mentor (TU Delft - Applied Probability)
J.M. Thijssen – Mentor (TU Delft - QN/Thijssen Group)
Johan Dubbeldam – Graduation committee member (TU Delft - Mathematical Physics)
N. Chepiga – Graduation committee member (TU Delft - QN/Chepiga Lab)
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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.