The Baxter–Bazhanov–Stroganov model: separation of variables and the Baxter equation

The Baxter–Bazhanov–Stroganov model (also known as the τ(2) model) has attracted much interest because it provides a tool for solving the integrable chiral -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(λ) 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 τ(2) model guarantee nontrivial solutions to the Baxter equations. For the N = 2 case, which is the free fermion point of a generalized Ising model, the Baxter equations are solved explicitly.