Partition Function of the Eight-Vertex Lattice Model

Abstract

The partition function of the zero-field``Eight-Vertex'' model on a square M by N lattice is calculated exactly in the limit of M, N large. This model includes the dimer, ice and zerofield Ising, F and KDP models as special cases. In general the free energy has a branch point singularity at a phase transition, with an irrational exponent. Academic Press

Yang–Baxter -operators and parameter permutations

“…On this level the operatorsŘ (1) andŘ (2) corresponding to these permutations are the elementary building blocks but the R-matrix is a composite object.…”

“…On this level the operators S i , i = 1, 2, 3 are elementary building blocks. Now the operatorsŘ (1) ,Ř (2) and R-matrix are composite objects. So we have the chain of inclusions with increasing symmetry…”

“…In Section 6 we construct the R-matrix and prove that it obeys the Yang-Baxter relation. In Section 7 we construct the operatorsŘ (1) andŘ (2) and prove the corresponding Yang-Baxter relations for them. Finally, in Section 8 we summarize.…”

“…The Yang-Baxter equation and its solutions play a key role in the theory of the completely integrable quantum models [1,2,3,4,5]. The general solution of the Yang-Baxter equation (R-matrix) is the operator R(u) acting in a tensor product V 1 ⊗ V 2 of two linear spaces.…”

Bethe equation of the τ(2)model and eigenvalues of a finite-size transfer matrix of a chiral Potts model with alternating rapidities

“…These results all rely on the technique of functional relations [17] about the transfer matrix and fusion matrices of the associated τ (2) -model in the extended study of chiral Potts model as a descendent of the six-vertex model found in [19]. The study is along the line of T Q-relation method invented by Baxter in solving the eigenvalue problem of the eight-vertex model [5,6,7]. The Q-matrix of the τ (2) -model considered is the chiral Potts transfer matrix.…”