We report computations of the short- and long-distance (scaling) contributions to the square-lattice Ising susceptibility. Both computations rely on summation of correlation functions, obtained using nonlinear partial difference equations. In terms of a temperature variable $\tau$, linear in ${T/T}_c-1\mathrm{}$, the short-distance terms have the form ${\tau }^p(\ln |\tau |{)}^q$ with $p\ge q^2$. A high- and low-temperature series of $N=323\mathrm{}$ terms, generated using an algorithm of complexity $\mathrm{O}\left(N^6\right)$, are analyzed to obtain the scaling part, which when divided by the leading $|\tau {|}^{-7/4\mathrm{}}$ singularity contains only integer powers of $\tau$. Contributions of distinct irrelevant variables are identified and quantified at leading orders $|\tau {|}^{9/4}$ and $|\tau {|}^{17/4}$.

• Received 22 August 2000

DOI:https://doi.org/10.1103/PhysRevLett.86.4120