Critical behaviour of the two-dimensional Ising susceptibility

Details Critical behaviour of the two-dimensional Ising susceptibility Critical behaviour of the two-dimensional Ising susceptibility

2000-09-05

arxiv.org/abs/cond-mat/0009059v1

Phys. Rev. Lett. 86 (2001) 4120-4123.

Physics

Condensed Matter

Statistical Mechanics

11 pages, REVTex 4

Scientific paper

10.1103/PhysRevLett.86.4120

We report computations of the short-distance and the long-distance (scaling) contributions to the square-lattice Ising susceptibility in zero field close to T_c. Both computations rely on the use of nonlinear partial difference equations for the correlation functions. By summing the correlation functions, we give an algorithm of complexity O(N^6) for the determination of the first N series coefficients. Consequently, we have generated and analysed series of length several hundred terms, generated in about 100 hours on an obsolete workstation. In terms of a temperature variable, \tau, linear in T/T_c-1, the short-distance terms are shown to have the form \tau^p(ln|\tau|)^q with p>=q^2. To O(\tau^14) the long-distance part divided by the leading \tau^{-7/4} singularity contains only integer powers of \tau. The presence of irrelevant variables in the scaling function is clearly evident, with contributions of distinct character at leading orders |\tau|^{9/4} and |\tau|^{17/4} being identified.

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