Subdominant critical indices for the ferromagnetic susceptibility of the spin-1/2 Ising model

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Abstract
Starting from the high-temperature series for the susceptibility of the spin-1/2 ferromagnetic Ising models-square, planar triangular, SC, BCC, FCC, diamond, and HSC in four, five and six dimensions-the authors analyse the analytical structure near the critical point of the susceptibility by writing it as a Laplace transform in the variable log (1-w/wc), where w=tanh( beta J). The interest of the method is that the coalescing singularities which sit at w=wc are spread out and can be analysed separately, the first subdominant critical indices, appearing as stable poles of Pade approximants. They first recover the results for the two-dimensional models, with a high accuracy: gamma =1.74995 and gamma s=0.757. The most stable results in three dimensions are obtained for the diamond lattice: gamma =1.2506+or-0.0015 and gamma s=0.42+or-0.11. The other lattices give 0.10<gamma ss=0.75.