FUNCTIONAL RELATIONS FOR TRANSFER MATRICES OF THE CHIRAL POTTS MODEL

1990 ◽  
Vol 04 (05) ◽  
pp. 803-870 ◽  
Author(s):  
R.J. Baxter ◽  
V.V. Bazhanov ◽  
J.H.H. Perk
Keyword(s):  
Potts Model ◽  
Finite Size ◽  
State Model ◽  
Integrable Case ◽  
Vertex Model ◽  
Chiral Potts Model ◽  
Transfer Matrices ◽  
Functional Relations ◽  
Finite Size Corrections

It has recently been shown that the solvable N-state chiral Potts model is related to a vertex model with N-state spins on vertical edges, two-state spins on horizontal edges. Here we generalize this to a “j-state by N-state” model and establish three sets of functional relations between the various transfer matrices. The significance of the “super-integrable” case of the chiral Potts model is discussed, and results reported for its finite-size corrections at criticality.

CYCLIC MONODROMY MATRICES FOR THE R-MATRIX OF THE SIX-VERTEX MODEL AND THE CHIRAL POTTS MODEL WITH FIXED SPIN BOUNDARY CONDITIONS

1992 ◽  
Vol 07 (supp01b) ◽  
pp. 963-975 ◽  
Author(s):  
VITALY O. TARASOV
Keyword(s):  
Boundary Conditions ◽  
Potts Model ◽  
Vertex Model ◽  
Chiral Potts Model ◽  
Transfer Matrices ◽  
Direct Computation ◽  
R Matrix ◽  
Monodromy Matrices

Irreducible cyclic representations of the algebra of monodromy matrices corresponding to the R-matrix of the six-vertex model are described. As a consequence, the direct computation of spectra for transfer-matrices of the chiral Potts model with special fixed-spin boundary conditions is done. The generalization of simple Baxter's Hamiltonian is proposed.

Chiral Potts model as a descendant of the six-vertex model

1990 ◽  
Vol 59 (3-4) ◽  
pp. 799-817 ◽  
Author(s):  
V. V. Bazhanov ◽  
Yu. G. Stroganov
Keyword(s):  
Potts Model ◽  
Vertex Model ◽  
Chiral Potts Model

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".

ZERO-TEMPERATURE SKEWED CHIRAL POTTS MODEL

1994 ◽  
Vol 06 (05a) ◽  
pp. 869-885
Author(s):  
R. J. BAXTER
Keyword(s):  
Potts Model ◽  
Shift Operator ◽  
Temperature Limit ◽  
Zero Temperature ◽  
Chiral Potts Model ◽  
Functional Relations ◽  
Spurious Solutions ◽  
Intermediate Phases ◽  
Free Interfaces ◽  
Ice Model

Functional relations have previously been obtained for the eigenvalues of the transfer matrices of the chiral Potts model. Introducing skewed boundary conditions is equivalent to merely modifying the quantum number of the spin shift operator in the relations (which accounts for at least some of the previously noted "spurious solutions"). As a first step towards calculating the general interfacial tension, we consider the model in a zero-temperature limit. It is still non-trivial, there being near-vertical free interfaces separating domains of different spin value. These interfaces behave like the "lines of down arrows" in the ice model, so one may hope to follow Lieb and use the Bethe ansatz to evaluate the partition function. It turns out that this can indeed be done. There is no wetting of an interface by intermediate phases.

scholarly journals Geometry, thermodynamics, and finite-size corrections in the critical Potts model

1999 ◽  
Vol 60 (6) ◽  
pp. 6491-6495 ◽  
Author(s):  
Chin-Kun Hu ◽  
Jau-Ann Chen ◽  
N. Sh. Izmailian ◽  
P. Kleban
Keyword(s):  
Potts Model ◽  
Finite Size ◽  
Finite Size Corrections
Sign in / Sign up

Export Citation Format

Share Document