Theoretical and Mathematical Physics

, Volume 109, Issue 3, pp 1590–1607 | Cite as

Solution of the 2D ising model on a triangular lattice by the method of auxiliaryq-deformed Grassmann fields

  • E. A. Bugrii


A representation in the form of a functional integral is obtained for the partition function of the inhomogeneous 2D Ising model on a triangular lattice where the coupling parameters are arbitrary functions of coordinates. The method for transforming the partition function into an integral uses an auxiliary six-component Grassmann field in which the Grassmann fields corresponding to one of the components commute with the others. Thus, one pair of components realizes a representation of the q-deformed group SLq(2, R) with q=−1 and the other two pairs correspond to the usual Grassmann spinors (q=1). An explicit expression in terms of the modified Pfaffian is found for the Gaussian integral over these fields and its relation to the ordinary Grassmann functional integral is established.


Partition Function Explicit Expression Arbitrary Function Ising Model Coupling Parameter 
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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • E. A. Bugrii
    • 1
  1. 1.N. N. Bogoliubov Institute of Theoretical PhysicsUkrainian Academy of SciencesUSSR

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