Partition Function of Six-vertex Model

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Raoufi, Aran | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 45884 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Zohuri-Zangeneh, Bijan
Abstract:
The six-vertex model is one of the lattice models of two dimensional statistical physics. In this model, like other models in statistical physics, the probability of occurrence of any configuration is proportional to the product of some local weights.The partition function of the model is the sum of products of local weights over all of the allowable configurations. The partition function has important physical interpretations and computing it is regarded as the first step toward the understanding of the model. In this thesis, we give a survey on different methods of calculating the partition functions. The important point is the generality of these methods such as employing Yang-Baxter equation and Bethe Ansatz for a broader range of models in statistical physics which are called integrable models. By analyzing and comparing these methods we get a better understanding of the concept of integrability.Through analyzing partition functions we also get a better understanding of the two combinatorial objects: alternating sign matrices and domino tiling and answer some important questions about them
Keywords:
Partition Function ; Statistical Physics ; Six Vertex Model ; Alternative Sign Matrix ; Domino Tiling ; Bethe Ansatz