Approximating the monomer-dimer constants through matrix permanent

Details Approximating the monomer-dimer constants through matrix permanent Approximating the monomer-dimer constants through matrix permanent

2007-08-13

arxiv.org/abs/0708.1641v2

Physics

Condensed Matter

Statistical Mechanics

6 pages, 2 figures

Scientific paper

10.1103/PhysRevE.77.016706

The monomer-dimer model is fundamental in statistical mechanics. However, it is $#P$-complete in computation, even for two dimensional problems. A formulation in matrix permanent for the partition function of the monomer-dimer model is proposed in this paper, by transforming the number of all matchings of a bipartite graph into the number of perfect matchings of an extended bipartite graph, which can be given by a matrix permanent. Sequential importance sampling algorithm is applied to compute the permanents. For two-dimensional lattice with periodic condition, we obtain $ 0.6627\pm0.0002$, where the exact value is $h_2=0.662798972834$. For three-dimensional lattice with periodic condition, our numerical result is $ 0.7847\pm0.0014$, {which agrees with the best known bound $0.7653 \leq h_3 \leq 0.7862$.}

Affiliated with

Also associated with

No associations

Rating

Approximating the monomer-dimer constants through matrix permanent 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 Approximating the monomer-dimer constants through matrix permanent, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Approximating the monomer-dimer constants through matrix permanent will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-23091