Corner transfer matrices of the chiral Potts model. II. The triangular lattice

1993 ◽  
Vol 70 (3-4) ◽  
pp. 535-582 ◽  
Author(s):  
R. J. Baxter
Keyword(s):  
Potts Model ◽  
Triangular Lattice ◽  
Chiral Potts Model ◽  
Transfer Matrices ◽  
Corner Transfer Matrices

CHIRAL POTTS MODEL: CORNER TRANSFER MATRICES AND PARAMETRIZATIONS

1993 ◽  
Vol 07 (20n21) ◽  
pp. 3489-3500 ◽  
Author(s):  
R.J. BAXTER
Keyword(s):  
Transfer Matrix ◽  
Potts Model ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Weight Functions ◽  
Chiral Potts Model ◽  
Transfer Matrices ◽  
Corner Transfer Matrices ◽  
Difference Property ◽  
The Difference

We consider the star-triangle relation and the form of its solutions. We present some simple parametrizations of the weight functions of the three-state chiral Potts model. This model does not have the “difference property”: we discuss the resulting difficulties in attempting to use the corner transfer matrix method for this model.

Nn(n–1)/2-STATE INTERTWINER RELATED TO Uq(sl(n)) ALGEBRA AT q2N=1

1992 ◽  
Vol 07 (30) ◽  
pp. 2827-2835
Author(s):  
R. M. KASHAEV ◽  
V. V. MANGAZEEV
Keyword(s):  
Statistical Model ◽  
Potts Model ◽  
Algebraic Curves ◽  
Baxter Equation ◽  
Matrix Elements ◽  
Chiral Potts Model ◽  
Transfer Matrices ◽  
R Matrix ◽  
High Genus

The Nn(n–1)/2-state R-matrix related to U q( sl (n)) algebra at q2N=1 is presented. Its matrix elements are interpreted as Boltzmann weights of an elementary box of some 2D lattice statistical model and given in terms of [Formula: see text] weights of the "minimal" sl (n) chiral Potts model. The corresponding family of transfer matrices depends on n rapidity variables living on high genus algebraic curves, the latter being defined by n moduli. The Yang-Baxter equation is conjectured to hold.

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.

scholarly journals Parallel family trees for transfer matrices in the Potts model

2015 ◽  
Vol 187 ◽  
pp. 55-71 ◽  
Author(s):  
Cristobal A. Navarro ◽  
Fabrizio Canfora ◽  
Nancy Hitschfeld ◽  
Gonzalo Navarro
Keyword(s):  
Potts Model ◽  
Transfer Matrices ◽  
Family Trees
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