Solution of the 2D ising model on a triangular lattice by the method of auxiliaryq-deformed Grassmann fields
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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.
KeywordsPartition Function Explicit Expression Arbitrary Function Ising Model Coupling Parameter
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- 1.H. W. J. Blöte and M. P. Nightingale,Phys. Rev. B,47, 15047 (1993).Google Scholar
- 2.C. Domb,Adv. Phys.,9, No. 34 (1960).Google Scholar
- 3.E. S. Fradkin and D. M. Shteingradt,Nuovo Cimento A,47, No. 1, 115 (1978).Google Scholar
- 4.A. I. Bugrii, “A simple fermionization method for the two-dimensional Ising model,” Preprint ITF-83-77P, Institute of Theoretical Physics, Kiev (1983).Google Scholar
- 5.V. M. Plechko,Theor. Math. Phys.,64, 748 (1985).Google Scholar
- 6.A. I. Bugrii and V. N. Shadura,Theor. Math. Phys.,103, 638 (1995).Google Scholar
- 7.M. Jimbo and T. Miwa, “Algebraic analysis of solvable lattice models,” Preprint RIMS-981, Kyoto Univ., Kyoto (1994).Google Scholar
- 8.F. A. Berezin,Usp. Mat. Nauk,24, No. 3, 3 (1969).Google Scholar
- 9.G. H. Wannier,Phys. Rev.,79, 357 (1950).Google Scholar
- 10.F. R. Gantmakher,Applications of the Theory of Matrices, Wiley, New York (1959).Google Scholar