Separation of variables in the Baxter-Bazhanov-Stroganov model
The Baxter-Bazhanov-Stroganov model (also known as the t2 model) has attracted much interest because it provides a tool for solving the integrable chiral ZN-Potts model. It can be formulated as a face spin model or via cyclic L-operators. Using the latter formulation and the Sklyanin-Kharchev-Lebedev approach, we give the explicit derivation of the eigenvectors of the component Bn(l) of the monodromy matrix for the fully inhomogeneous chain of finite length. For the periodic chain we obtain the Baxter T-Q-equations via separation of variables. The functional relations for the transfer-matrices of the t2 model guarantee non-trivial solutions to the Baxter equations. For the N=2 case, which is free fermion point of a generalized Ising model, the Baxter equations are solved explicitly. These solutions give explicit formulas for eigenvectors of Ising transfer-matrix. Using them, we proved formula for form-factors in the Ising model on finite lattice.
Joint work with G. von Gehlen, S. Pakuliak, V. Shadura, Yu. Tykhyy.