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):  
1992 ◽  
Vol 06 (14) ◽  
pp. 2559-2574 ◽  
Author(s):  
S. BOUKRAA ◽  
J.-M. MAILLARD

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.


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

1997 ◽  
Vol 11 (01n02) ◽  
pp. 213-221 ◽  
Author(s):  
Claude-M. Viallet

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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