q-Deformed grassmann fields and the two-dimensional Ising model |
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Authors: | A I Bugrij V N Shadura |
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Institution: | (1) Bogolyubov Institute for Theoretical Physics, 252142 Kiev, Ukraine |
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Abstract: | We construct an exact representation of the Ising partition function in the form of the SLq(2, R)-invariant functional integral for the lattice-free q-fermion field theory (q=–1). It is shown that the q-fermionization allows one to rewrite the partition function of the eight-vertex model in an external field through a functional integral with four-fermion interaction. To construct these representations, we define a lattice (l, q, s)-deformed Grassmann bispinor field and extend the Berezin integration rules to this field. At q=–1, l=s=1, we obtain the lattice q-fermion field which allows us to fermionize the two-dimensional Ising model. We show that the Gaussian integral over (q, s)-Grassmann variables is expressed through the (q, s)-deformed Pfaffian which is equal to square root of the determinant of some matrix at q=±1, s=±1.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 103, No. 3, pp. 388–412. June, 1995. |
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