Abstract
Some formulas are given for the asymptotic form of NXN modified block Toeplitz determinants for large N. These formulas are useful in obtaining the asymptotic behaviors of the correlation function of two spins of the Ising model on a two-dimensional regular lattice when the two spins are not on an axis. l ) developed a mathematical theory for the asymptotic behavior of the NXN Toeplitz determinant for large N_ For the Ising model on the general two-dimensional regular lattice, the spin pair correlation function of two spins on an axis is generally express ed by a block Toeplitz determinant. Many authors2)-4) extended Wu's theory to the block Toeplitz determinant and discussed the asymptotic behavior of the correlation function. When two spins are not on an axis, the spin pair correlation function is generally expressed by a modified block Toeplitz determinant of the form: ml n. n n mr columns ~ ~ ~ ~ ~
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