Cluster expansion and generalized transfer matrices for the statistical mechanics of linear chains

1981 ◽  
Vol 24 (4) ◽  
pp. 555-586 ◽  
Author(s):  
Douglas J. Klein ◽  
Terry L. Welsher
Keyword(s):  
Statistical Mechanics ◽  
Cluster Expansion ◽  
Transfer Matrices ◽  
Linear Chains

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".

scholarly journals Statistical mechanics of self-gravitating system: Cluster expansion method

1999 ◽  
Vol 260 (1-2) ◽  
pp. 4-9 ◽  
Author(s):  
Osamu Iguchi ◽  
Tomomi Kurokawa ◽  
Masahiro Morikawa ◽  
Akika Nakamichi ◽  
Yasuhide Sota ◽  
...  
Keyword(s):  
Statistical Mechanics ◽  
Cluster Expansion ◽  
Expansion Method ◽  
Cluster Expansion Method
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