Methods of Series Analysis. II. Generalized and Extended Methods with Application to the Ising Model

Abstract

Several new general methods of series analysis are introduced and tested on an assortment of known functions. These methods are then applied to several of the series expansions known for the thermodynamic properties of the spin-\textonehalf{} Ising model. We are able to obtain an unbiased analysis of the high-temperature specific-heat singularity, and find $\ensuremath{\alpha}\ensuremath{\approx}0.13\ifmmode\pm\else\textpm\fi{}0.01$. The application of our methods in other cases generally agrees with that of previous workers. Our methods in practice amount to procedures for looking more closely at the dominant singularity, at the expense of accuracy for competing singularities. For certain types of function, thought to occur in the study of critical phenomena, our methods are noticeably more effective than those previously employed.