Pad$eacute$ approximant analysis of the Ising model specific heat above the Curie temperature

The suggestion is made that one would not expect the usual Padé approximant analysis of the high-temperature Ising model specific heat expansion to agree with the ratio method results. An argument is given which suggests that for close-packed lattices the singularity in the specific heat is not transformed into a simple pole unless one first differentiates twice with respect to the expansion variable. The usual Padé approximant procedure is then applied to both the specific heat series and its second derivative. The results are contrasted and they are found to be at variance with one another. The analysis of the second derivative agrees better with the ratio results. Similar arguments are presented for the loose-packed lattices and qualitatively similar results are obtained. The evidence supports the conclusion of Sykes, Martin and Hunter that the critical index α is equal to fraction one-eighth.