Journal article

Experimental mathematics on the magnetic susceptibility of the square lattice Ising model

S Boukraa, AJ Guttmann, S Hassani, I Jensen, J-M Maillard, B Nickel, N Zenine

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | IOP PUBLISHING LTD | Published : 2008

Abstract

We calculate very long low- and high-temperature series for the susceptibility χ of the square lattice Ising model as well as very long series for the five-particle contribution χ(5) and six-particle contribution χ(6). These calculations have been made possible by the use of highly optimized polynomial time modular algorithms and a total of more than 150 000 CPU hours on computer clusters. The series for χ (low- and high-temperature regimes), χ(5) and χ(6) are now extended to 2000 terms. In addition, for χ(5), 10 000 terms of the series are calculated modulo a single prime, and have been used to find the linear ODE satisfied by χ(5) modulo a prime. A diff-Padé analysis of the 2000 terms seri..

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