The Library
Ising-Kac models near criticality
Tools
Tools
Tools
Iberti, Massimo (2018) Ising-Kac models near criticality. PhD thesis, University of Warwick.
|
PDF
WRAP_Theses_Iberti_2018.pdf - Submitted Version - Requires a PDF viewer. Download (1712Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3228143~S15
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.
| Item Type: | Thesis (PhD) | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Stochastic partial differential equations, Ising model, Ferromagnetism -- Mathematics, Magnetization -- Mathematical models, Besov spaces, Mathematical physics | ||||
| Official Date: | 2018 | ||||
| Dates: |
|
||||
| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Hairer, Martin | ||||
| Format of File: | |||||
| Extent: | v, 191 leaves | ||||
| Language: | eng |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
