A method for calculating the long-range behavior of the spin correlator in a two-dimensionalising model

A method is developed for studying the long-range behavior of the spin correlator in a two-dimensional Ising model, based on an approximate solving of the equation for the resolvent of a Toeplitz matrix whose determinant is a correlator. In the scaling domain the answer is expressed in terms of the Green's functions of certain singular equations. The bounds obtained for the norm of the matrix-resolvent yield the possibility of a rigorous justification of the asymptotic formulas.