Determination of critical behaviour in lattice statistics from series expansions II

Abstract

A method is developed for determining the critical point and the critical exponent from terms in the series expansion of a function. For low temperature Ising model series the method provides an alternative technique to the method of Padé approximants. Application to some high and low temperature series for the Ising model on a simple cubic and a diamond lattice suggest the following exponents: γ = 1·2500 ± 0·0002, γprime = 1·29 ± 0·04, β = 0·312 ± 0·002 and αprime = 0·13 ± 0·07 for the high and low temperature susceptibility, the spontaneous magnetization and the low temperature specific heat respectively. These results are largely in agreement with previous analyses. Show more