School of Mathematics and Statistics - Research Publications

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Subject: Mathematical Logic × Subject: Lattices and Combinatorics ; Mathematical Sciences × Author: Guttmann, Anthony ×

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    Vicious walkers, friendly walkers, and young tableaux. III. Between two walls
    Krattenthaler, C ; Guttmann, AJ ; Viennot, XG (SPRINGER, 2003-03-01)
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    Critical behavior of the two-dimensional Ising susceptibility
    Orrick, WP ; Nickel, BG ; Guttmann, AJ ; Perk, JHH (AMERICAN PHYSICAL SOC, 2001-04-30)
    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).