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Algorithmic proof for the completeness of the two-dimensional Ising model

Karimipour, V ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1103/PhysRevA.86.052303
  3. Publisher: 2012
  4. Abstract:
  5. We show that the two-dimensional (12D) Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all its spin-spin coupling equal to iπ4 and all parameters of the original model are contained in the local magnetic fields of the Ising model. This result has already been derived by using techniques from quantum information theory and by exploiting the universality of cluster states. Here we do not use the quantum formalism and hence make the completeness result accessible to a wide audience. Furthermore, our method has the advantage of being 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
  6. Keywords:
  7. 2D Ising model ; 2D lattice ; Cluster state ; Complex-coupling ; Discrete lattices ; Lattice models ; Local magnetic field ; Original model ; Partition functions ; Quantum information theory ; Spin-spin couplings ; Two-dimensional ising model ; Algorithms ; Crystal lattices ; Information theory ; Two dimensional ; Ising model
  8. Source: Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 86, Issue 5 , 2012 ; 10502947 (ISSN)
  9. URL: http://journals.aps.org/pra/abstract/10.1103/PhysRevA.86.052303