15 papers · 1 filter
Dimer lambda_d Expansion, A Contour Integral Stationary Point Argument
Paul Federbush
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 lar…
Dimer lambda_d Expansion, Dimensional Dependence of J_n Kernels
Paul Federbush
In previous papers an asymptotic expansion for the dimer lambda_d of the form lambda_d ~ (1/2)ln(2d) - 1/2 + c_1/d + c_2/d^2 ... was developed. Kernels J_n were a key ingredient in…
Dimer lambda_3 = .453 +/- .001 and Some Other Very Intelligent Guesses
Paul Federbush
Working with a presumed asymptotic series for lambda_d developed in previous work, we make some intelligent guesses for lambda_d with d=3, 4, 5; and estimates for the corresponding…
Dimer lambda_d Expansion Computer Computations
Paul Federbush
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 qu…
Hidden Structure in Tilings, Conjectured Asymptotic Expansion for lambda_d in Multidimensional Dimer Problem
Paul Federbush
The dimer problem arose in a thermodynamic study of diatomic molecules, and was abstracted into one of the most basic and natural problems in both statistical mechanics and combina…
Tilings With Very Elastic Tiles
Paul Federbush
We consider tiles of some fixed size, with an associated weighting on the shapes of tile, of total mass 1. We study the pressure, , of tilings with those tiles; the pressure, on…