The paper conjectures an asymptotic form for Mayer series coefficients b(n) on regular lattices and reports good numerical agreement when fitting four parameters to the first 20 known coefficients on several bipartite lattices.
Dimer lambda_d Expansion, Dimensional Dependence of J_n Kernels
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abstract
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 the theory. Herein we prove J_n are of the form J_n = C_r/d^r + C_(r+1)/d^(r+1) + ... + C_(n-1)/d^(n-1) with r > (n/2)-1.
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The Aesthetic Asymptotics of the Mayer Series Coefficients for a Dimer Gas on a Regular Lattice
The paper conjectures an asymptotic form for Mayer series coefficients b(n) on regular lattices and reports good numerical agreement when fitting four parameters to the first 20 known coefficients on several bipartite lattices.