Boundary correlation function of fixed-to-free bcc operators in square-lattice Ising model
Statistical Mechanics
2009-11-11 v1 Mathematical Physics
math.MP
Abstract
We calculate the boundary correlation function of fixed-to-free boundary condition changing operators in the square-lattice Ising model. The correlation function is expressed in four different ways using block Toeplitz determinants. We show that these can be transformed into a scalar Toeplitz determinant when the size of the matrix is even. To know the asymptotic behavior of the correlation function at large distance we calculate the asymptotic behavior of this scalar Toeplitz determinant using the Szeg\"o's theorem and the Fisher-Hartwig theorem. At the critical temperature we confirm the power-law behavior of the correlation function predicted by conformal field theory.
Keywords
Cite
@article{arxiv.cond-mat/0612102,
title = {Boundary correlation function of fixed-to-free bcc operators in square-lattice Ising model},
author = {Seung-Yeop Lee},
journal= {arXiv preprint arXiv:cond-mat/0612102},
year = {2009}
}