The boundary correlation function of fixedtofree boundaryconditionchanging operators in a squarelattice Ising model
Abstract
We study the boundary correlation function of the fixedtofree boundaryconditionchanging (bcc) operators in the squarelattice Ising model. First, we find a formula for representing a large class of twopoint boundary correlation functions using a 2 × 2 block Toeplitz determinant. Using this formula the correlation function of the fixedtofree 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.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 October 2007
 DOI:
 10.1088/17425468/2007/10/P10011
 arXiv:
 arXiv:condmat/0612102
 Bibcode:
 2007JSMTE..10...11L
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Mathematical Physics;
 Mathematics  Mathematical Physics