scholarly journals Semi-Classical Analysis of Non-Self-Adjoint Transfer Matrices in Statistical Mechanics I

2015 ◽  
Vol 17 (2) ◽  
pp. 437-458 ◽  
Author(s):  
Margherita Disertori ◽  
Sasha Sodin
Keyword(s):  
Statistical Mechanics ◽  
Transfer Matrices ◽  
Classical Analysis

Star-Triangle and Star-Star Relations in Statistical Mechanics

1997 ◽  
Vol 11 (01n02) ◽  
pp. 27-37 ◽  
Author(s):  
R. J. Baxter
Keyword(s):  
Statistical Mechanics ◽  
Potts Model ◽  
Original Model ◽  
State Model ◽  
Nearest Neighbour ◽  
Transfer Matrices ◽  
Zamolodchikov Model ◽  
Adequate Condition

The homogeneous three-layer Zamolodchikov model is equivalent to a four-state model on the checkerboard lattice which closely resembles the four-state critical Potts model, but with some of its Boltzmann weights negated. Here we show that it satisfies a "star-to-reverse-star" (or simply star-star) relation, even though we know of no star-triangle relation for this model. For any nearest-neighbour checkerboard model, we show that this star-star relation is sufficient to ensure that the decimated model (where half the spins have been summed over) satisfies a "twisted" Yang-Baxter relation. This ensures that the transfer matrices of the original model commute in pairs, which is an adequate condition for "solvability".

COMMUTING TRANSFER MATRICES AND LINK POLYNOMIALS

1992 ◽  
Vol 03 (02) ◽  
pp. 205-212 ◽  
Author(s):  
V.F.R. JONES
Keyword(s):  
Statistical Mechanics ◽  
Transfer Matrices ◽  
Crossing Numbers ◽  
Commuting Transfer Matrices

Borrowing from an argument in statistical mechanics we give a machine for constructing pairs of links with the same skein polynomials. Examples are generally not mutants (Kauffman polynomials differ) and can have small crossing numbers, e.g. the coincidence V41 #41 = V89, is explained.

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