Finite-lattice form factors in free-fermion models

Abstract

We consider the general -symmetric free-fermion model on the finite periodic lattice, which includes as specialcases the Ising model on the square and triangular lattices and the -symmetric BBS τ(2)-model with n = 2. Translating Kaufman’s fermionic approach to diagonalization of Ising-like transfermatrices into the language of Grassmann integrals, we determine the transfermatrix eigenvectors and observe that they coincide with the eigenvectors of asquare lattice Ising transfer matrix. This allows us to find exact finite-latticeform factors of spin operators for the statistical model and the associatedfinite-length quantum chains, of which the most general is equivalent to theXY chain in a transverse field.