Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.759685
Title: Ising-Kac models near criticality
Author: Iberti, Massimo
ISNI:       0000 0004 7431 714X
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2018
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Abstract:
The present thesis consists in an investigation around the result shown by H. Weber and J.C. Mourrat in [MW17a], where the authors proved that the fluctuation of an Ising models with Kac interaction under a Glauber-type dynamic on a periodic two-dimensional discrete torus near criticality converge to the solution of the Stochastic Quantization Equation Φ 4/2. In Chapter 2, starting from a conjecture in [SW16], we show the robustness of the method proving the convergence in law of the fluctuation field for a general class of ferromagnetic spin models with Kac interaction undergoing a Glauber dynamic near critical temperature. We show that the limiting law solves an SPDE that depends heavily on the state space of the spin system and, as a consequence of our method, we construct a spin system whose dynamical fluctuation field converges to Φ 2n/2. In Chapter 3 we apply an idea by H. Weber and P. Tsatsoulis employed in [TW16], to show tightness for the sequence of magnetization fluctuation fields of the Ising-Kac model on a periodic two-dimensional discrete torus near criticality and characterise the law of the limit as the Φ 4/2 measure on the torus. This result is not an immediate consequence of [MW17a]. In Chapter 4 we study the fluctuations of the magnetization field of the Ising-Kac model under the Kawasaki dynamic at criticality in a one dimensional discrete torus, and we provide some evidence towards the convergence in law to the solution to the Stochastic Cahn-Hilliard equation.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.759685  DOI: Not available
Keywords: QA Mathematics
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