Matching Measure, Benjamini–Schramm Convergence and the Monomer–Dimer Free Energy
Name
10955_2015_Article_1309.pdf
Size
549.72 KB
Format
Adobe PDF
Checksum (MD5)
2c9bad9835e7778fe6f54d595463610d
Author(s)
Abért, Miklós
Hubai, Tamás
Csikvari, Peter
Date Issued
July 2015
Journal
Journal of Statistical Physics
Publisher
Springer US
Citation
Abért, Miklós, Péter Csikvári, and Tamás Hubai. “Matching Measure, Benjamini–Schramm Convergence and the Monomer–Dimer Free Energy.” Journal of Statistical Physics 161.1 (2015): 16–34.
Version
Author's final manuscript
Abstract
We define the matching measure of a lattice L as the spectral measure of the tree of self-avoiding walks in L. We connect this invariant to the monomer–dimer partition function of a sequence of finite graphs converging to L. This allows us to express the monomer–dimer free energy of L in terms of the matching measure. Exploiting an analytic advantage of the matching measure over the Mayer series then leads to new, rigorous bounds on the monomer–dimer free energies of various Euclidean lattices. While our estimates use only the computational data given in previous papers, they improve the known bounds significantly.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10955-015-1309-7
