An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem

Details An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem

2010-11-30

arxiv.org/abs/1011.6579v3

Journal of Statistical Physics: Volume 143, Issue 2 (2011), p. 306

Physics

Mathematical Physics

15 pages, much more about d=1,2,3

Scientific paper

Let (lambda_d)(p) be the p monomer-dimer entropy on the d-dimensional integer lattice Z^d, where p in [0,1] is the dimer density. We give upper and lower bounds for (lambda_d)(p) in terms of expressions involving (lambda_(d-1))(q). The upper bound is based on a conjecture claiming that the p monomer-dimer entropy of an infinite subset of Z^d is bounded above by (lambda_d)(p). We compute the first three terms in the formal asymptotic expansion of (lambda_d)(p) in powers of 1/d. We prove that the lower asymptotic matching conjecture is satisfied for (lambda_d)(p).

Affiliated with

Also associated with

No associations

Rating

An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-445652