The boundary correlation function of fixed-to-free boundary-condition-changing operators in a square-lattice Ising model
We study the boundary correlation function of the fixed-to-free boundary-condition-changing (bcc) operators in the square-lattice Ising model. First, we find a formula for representing a large class of two-point boundary correlation functions using a 2 × 2 block Toeplitz determinant. Using this formula the correlation function of the fixed-to-free bcc operator is represented using block Toeplitz determinants, for arbitrary, uniformly anisotropic couplings. This block Toeplitz determinant is transformed into a scalar Toeplitz determinant when the size of the matrix is an even number. We use Szegö's theorem and the Fisher Hartwig theorem to identify the asymptotic behavior of this scalar Toeplitz determinant.