Critical behavior of the two-dimensional Ising susceptibility

We report computations of the short- and long-distance (scaling) contributi ons to the square-lattice Ising susceptibility. Both computations rely on s ummation of correlation functions, obtained using nonlinear partial differe nce equations. In terms of a temperature variable tau, linear in T/T-c - 1, the short-distance terms have the form tau (p)(In\tau\)(q) with p greater than or equal to q(2). A high- and low-temperature series of N = 323 terms, generated using an algorithm of complexity O(N-6), are analyzed to obtain the scaling part, which when divided by the leading \tau\(-7/4) singularity contains only integer powers of tau. Contributions of distinct irrelevant variables are identified and quantified at leading orders \tau\(9/4) and \t au\(17/4).