Q-deformed Grassmann fields and the two-dimensional Ising model

Journal Article · Fri Dec 01 04:00:00 EST 1995 · Theoretical and Mathematical Physics

DOI:https://doi.org/10.1007/BF02065864· OSTI ID:244158

Bugrij, A I; Shadura, V N ^[1]

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1. Bogolyubov Inst. for Theoretical Physics, Kiev (Ukraine)

We construct an exact representation of the Ising partition function in the form of the SL{sub q} (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.

• Sponsoring Organization: USDOE
• OSTI ID: 244158
• Journal Information: Theoretical and Mathematical Physics, Journal Name: Theoretical and Mathematical Physics Journal Issue: 3 Vol. 103; ISSN TMPHAH; ISSN 0040-5779
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
BOUNDARY CONDITIONS
COMMUTATION RELATIONS
ISING MODEL
PARTITION FUNCTIONS
QUANTUM FIELD THEORY
SPINORS
TWO-DIMENSIONAL CALCULATIONS