Ising susceptibility series

The series below for chi_j were produced using Fortran programs written by Bernie Nickel and modified by me to perform the calculation in high precision arithmetic. The algorithm is described in two papers by Bernie Nickel,

Bernie Nickel, On the singularity structure of the 2D Ising model susceptibility, J. Phys. A: Math. Gen. 32 (1999) 3889-3906.
Bernie Nickel, Addendum to `On the singularity structure of the 2D Ising model susceptibility', J. Phys. A: Math. Gen. 33 (2000) 1693-1711.

I used David Bailey's high precision arithmetic package mpfun. The computations were performed on the Research SP at Indiana University.

1/16 chi₅ to order s¹⁸². The numbers listed are the coefficients of (s/2)ⁿ where n ranges from 24 to 182. The expansion variable is s=sinh 2K where K is the (isotropic) coupling constant divided by k_BT.

1/64 chi₆ to order (1/s)¹⁴⁰. The numbers listed are the coefficients of (1/(2s)^2)ⁿ where n ranges from 18 to 70.

1/256 chi₈ to order (1/s)¹³². The numbers listed are the coefficients of (1/(2s)^2)ⁿ where n ranges from 32 to 66.

1/256 chi₉ to order s¹⁴². The numbers listed are the coefficients of (s/2)ⁿ where n ranges from 80 to 142.

1/1024 chi₁₀ to order (1/s)¹⁵⁰. The numbers listed are the coefficients of (1/(2s)^2)ⁿ where n ranges from 50 to 75.

1/1024 chi₁₁ to order s¹⁶⁰. The numbers listed are the coefficients of (s/2)ⁿ where n ranges from 120 to 160.

1/4096 chi₁₂ to order (1/s)¹⁸². The numbers listed are the coefficients of (1/(2s)^2)ⁿ where n ranges from 72 to 91.

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This page last updated 20 March 2005.