Paul Federbush
Dimer Lambda_d Expansion Computer Computations
(12K, LaTeX)
ABSTRACT. In a previous paper an asymptotic expansion for lambda_d in
powers of 1/d was developed. The results of computer computations
for some terms in the expansion, as well as various quantities
associated to the expansion, are herein presented. The computations
(in integer arithmetic) are actually done only for d=1, d=2, and d=3,
but some results for arbitrary dimension follow from the general
structure of the theory. In particular we obtain the next term in
powers of 1/d, the 1/d^3 term in the asymptotic expansion for
lambda_d, as well as checking the correctness of the terms previously
calculated by hand.
For d=2 and d=3 a second expansion for lambda_d is defined and
numerically studied. Contrary to our hopes this second type of
expansion appears not to be convergent. There is not enough evidence
to argue if the expansions for lambda_d in powers of 1/d are
convergent for either d=2 or d=3, but likely they are not.
( Certainly convergence, but at a very slow rate, remains an
interesting possibility in all our cases. )