Dimer lambda_d Expansion, A Contour Integral Stationary Point Argument

Abstract

In the development of a presumed asymptotic expansion for lambda_d in previous work, a basic step involved extracting the asymptotic behavior of a sum as being dominated by the largest term in the sum. But this argument only is valid when the terms in the sum are positive. In the case terms in the sum are not all positive (some of the J_n are negative) we replace the `largest term' argument by the route of this paper. The sum is replaced by a contour integral. We then find a stationary point of the integrand that we conjecture dominates the asymptotic behavior of the integral.