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Application of Off-Critical Schramm-Loewner Evolution to Sandpile Models and Percolation

Nattagh Najafi, Morteza | 2012

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 42886 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Rouhani, Shahin; Moghimi, Saman
  7. Abstract:
  8. Schramm – Loewner Evolution (SLE) is a framework which helps to classify interfaces in critical models. At criticality two or more phases of the model are separated by an interface. In two dimensions this interface is a simple random curve, which can be addressed by SLE theory. This classification has crucial rule in our understanding of statistical models. In spite of our understanding of2 dimensional statistical models and 1+1dimensional quantum field theories, little workhas been done on these models out of criticality. In this thesis we focus on the Schramm-Loewner Evolutions and conformal field theoriesin vicinity of critical points. To this end we state the theories which the off-critical Schramm-Loewner evolution and perturbed conformal field theories correspond to.Using off-critical Schramm-Loewner Evolution,we show thatthe dissipative abeliansandpile model,corresponds to the self-avoiding walk (SAW)in scales much larger than the correlation length. We also show that a variety of SLE, namely SLE(κ,ρ), is more reliable tool for analyzing the interfaces of the critical statistical models. We apply this framework to critical percolation and abeliansandpile model.The sandpile model can become off-critical by modifying the toppling rule to an anisotropic one in such a way that one move from BTW model to Manna model perturbatively. The results of application of off-critical Schramm-Loewner evolution are analyzed and it is shown that this perturbation corresponds to a relevant perturbation of the action corresponding to the BTW model and the conformal weight of the perturbing filed is 1
  9. Keywords:
  10. Conformal Fields Theory ; Schramm-Loewner Evolution (SLE) ; Abelian Sandpile Model ; Percolation ; Critical Phenomena

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