Critical exponents for the general spin ising model using the rational approximation method
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The rational approximation method is used to investigate the problem of calculating the critical indices of the Ising model. The method is applied to several test cases thought to be similar to the Ising model and then is applied to the susceptibility of the general spin Ising model on the body centered cubic lattice. It is found that for one particular spin (S=0.73) convergence is rapid and smooth, allowing the estimate γ=1.2411 ± 0.0002 in agreement with the renormalization group and with recent analyses of the bcc series. If the existence or value of this ‘critical’ spin is not correct, or is not accepted, it is still possible to estimate γ=1.241 ± 0.001 if the universality of the subdominant index ϑ is assumed. Similar analysis of the series for the second moment correlation function M2, leads to the estimate v=0.6335 ± 0.0003 (for S=0.73). The implications of these results on the scaling and hyperscaling hypotheses are discussed.
KeywordsIsing Model Critical Exponent Chebyshev Polynomial Critical Index Pad8 Approximants
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