Conformal Invariance in the 2D Ising Model

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Khaledian, Arman | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 45804 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Esfahani Zadeh, Mostafa; Alishahi, Kasra
Abstract:
Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, self-avoiding polymers, . . .This has led to numerous exact (but non-rigorous) predictions of their scaling exponents and dimensions. We will discuss how to prove the conformal invariance conjectures, especially in relation to Schramm-Loewner Evolution
Keywords:
Stochastic Process ; Conformal Invariance ; Ising model ; Smirnov Theorem