scholarly journals Inversion relations, reciprocity and polyominoes

1999 ◽  
Vol 3 (2-4) ◽  
pp. 223-249 ◽  
Author(s):  
M. Bousquet-Mélou ◽  
A. J. Guttmann ◽  
W. P. Orrick ◽  
A. Rechnitzer
Keyword(s):  
Inversion Relations

TAXONOMY OF THE SIXTEEN-VERTEX MODELS

1992 ◽  
Vol 06 (14) ◽  
pp. 2559-2574 ◽  
Author(s):  
S. BOUKRAA ◽  
J.-M. MAILLARD
Keyword(s):  
Symmetry Group ◽  
Parameter Space ◽  
Vertex Model ◽  
Vertex Models ◽  
Exact Calculations ◽  
Inversion Relations

A classification of the subcases of the sixteen-vertex model compatible with the infinite symmetry group generated by the inversion relations of the model is performed. The elliptic parameterization of these models is recalled, emphasizing the subvarieties of the parameter space for which this parameterization degenerates into a rational one. This situation corresponds to the vanishing of some discriminant and is deeply related to the critical and disorder manifolds for these models. We concentrate on subcases of the sixteen-vertex model for which factorizations of this discriminant occur, allowing further exact calculations.

Inversion relations for exclusive and inclusive cross sections within the independent electron approximation

1998 ◽  
Vol 58 (3) ◽  
pp. 2148-2159 ◽  
Author(s):  
M. M. Sant’Anna ◽  
E. C. Montenegro ◽  
J. H. McGuire
Keyword(s):  
Cross Sections ◽  
Inversion Relations

Free Fermion Conditions and the Symmetries of Integrability

1997 ◽  
Vol 11 (01n02) ◽  
pp. 213-221 ◽  
Author(s):  
Claude-M. Viallet
Keyword(s):  
Free Fermion ◽  
Vertex Models ◽  
Inversion Relations

We show that free-fermion conditions on vertex models amount to degeneration conditions for the inversion relations and the symmetries of the Yang-Baxter equations. We also show how solutions of the tetrahedron equations enjoy a similar property, and analyze the phenomenon.

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