Seung-Yeop Lee J. Stat. Mech. (2007) P10011 doi:10.1088/1742-5468/2007/10/P10011
Seung-Yeop Lee
Show affiliationsWe 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.
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
47L80 Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)
15A15 Determinants, permanents, other special matrix functions (See also 19B10, 19B14)
Issue 10 (October 2007)
Received 23 August 2007, accepted for publication 28 September 2007
Published 22 October 2007
Seung-Yeop Lee J. Stat. Mech. (2007) P10011
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