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The Completeness in Statistical Mechanics

Zarei, Mohammad Hossein | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45199 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Karimipour, Vahid
  7. Abstract:
  8. Ising model. It means that the partition function of each lattice model is equal to the partition function of 2D Ising model. This completeness is proved by using concepts and techniques from quantum information theory and is based on the universality of cluster states. We have now proved this important result, by using independent and general concepts and methods which are accessible to a wide audience of researchers across many disciplines. Furthermore, our method has the advantage of eing algorithmic in nature so that, by following a set of simple graphical transformations, one is able to transform any discrete lattice model to an Ising model defined on a (polynomially) larger 2D lattice.The 2D Ising model is complete for discrete lattice models. We extend the quantum formalism of the partition function to continuous variable for the statistical mechanical models of discretized field theories on lattices and then show that the discrete version of ϕ4 theory on 2D square lattice is complete in the sense that the partition function of any other discretized scalar field theory on an arbitrary lattice with arbitrary interactions can be realized as a special case of the partition function of this model
  9. Keywords:
  10. Perfect ; Cluster State ; Computational Complexity ; Two Dimensional Ising Model ; Field Theory ; Partition Functions

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