Abstract
Adding a random magnetic field to the Curie-Weiss model adds a considerable amount of complexity to the model. The case when the random fields may take only a finite number of values is still tractable with lumping techniques. This case is treated in this chapter. In Sect. 14.1 we introduce the model. In Sect. 14.2 we define the associated Gibbs measure and the relevant order parameter. In Sect. 14.3 we define the Glauber dynamics and state the main metastability result. Section 14.4 deals with coarse-graining. We construct the effective Dirichlet form that is obtained after the coarse-graining. Section 14.5 studies the energy landscape near the critical points. Section 14.6 analyses the eigenvalues of the Hessian at the critical points, while Sect. 14.7 looks at the overall topology of the energy landscape.
He’s a wonderfully clever man, you know. Sometimes he says things that only the Other Professor can understand. Sometimes he says things that nobody can understand. (Lewis Carroll, Sylvie and Bruno)
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Bovier, A., den Hollander, F. (2015). The Curie-Weiss Model with a Random Magnetic Field: Discrete Distributions. In: Metastability. Grundlehren der mathematischen Wissenschaften, vol 351. Springer, Cham. https://doi.org/10.1007/978-3-319-24777-9_14
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DOI: https://doi.org/10.1007/978-3-319-24777-9_14
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