Critical behavior of the two-dimensional Ising susceptibility.
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/Tc-1, the short-distance terms have the form tau(p)(ln/tau/)q with p> or =q2. A high- and low-temperature series of N = 323 terms, generated using an algorithm of complexity O(N6), 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 /tau/(17/4).
Orrick
W P
WP
Department of Mathematics & Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia. worrick@ms.unimelb.edu.au
Nickel
B G
BG
Guttmann
A J
AJ
Perk
J H
JH