The susceptibility of the square lattice Ising model: New developments

We have made substantial advances in elucidating the properties of the susc eptibility of the square lattice Ising model. We discuss its analyticity pr operties, certain closed form expressions For subsets of the coefficients, and give an algorithm of complexity O(N-6) to determine its first N coeffic ients. As a result, we have generated and analyzed series with more than 30 0 terms in both the high- and low-temperature regime. We quantify the effec t of irrelevant variables to the scaling-amplitude functions. In particular , we find and quantify the breakdown of simple scaling, in the absence of i rrelevant scaling fields, arising first at order /T-T-c/(9/4), though high- low temperature symmetry is still preserved. At terms of order /T- T-c/(17/ 4) and beyond, this symmetry is no longer present. The short distance terms are shown to have the form (T-T-c)(p) (log /T-T-c/)(q) with p greater than or equal to q(2). Conjectured exact expressions for some correlation funct ions and series coefficients in terms of elliptic theta Functions also fore shadow future developments.