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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 Z N -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 B n (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 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.

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We continue our investigation of the Z N -Baxter-Bazhanov-Stroganov model using the method of separation of variables [1]. In this paper we calculate the norms and matrix elements of a local Z N -spin operator between eigenvectors of the auxiliary problem. For the norm the multiple sums over the intermediate states are performed explicitly. In the case N = 2 we solve the Baxter equation and obtain form-factors of the spin operator of the periodic Ising model on a finite lattice.

We continue our investigation of the Baxter-Bazhanov-Stroganov or τ (2)model using the method of separation of variables [1,2]. In this paper we derive for the first time the factorized formula for form-factors of the Ising model on a finite lattice conjectured previously by A. Bugrij and O. Lisovyy in [3,4]. We also find the matrix elements of the spin operator for the finite quantum Ising chain in a transverse field.