Matching Measure, Benjamini–Schramm Convergence and the Monomer–Dimer Free Energy
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 th...
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| Format: | Article |
| Language: | English |
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Springer US
2016
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| Online Access: | http://hdl.handle.net/1721.1/104881 https://orcid.org/0000-0002-1594-9206 |
| _version_ | 1811074368105611264 |
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| author | Abért, Miklós Hubai, Tamás Csikvari, Peter |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Abért, Miklós Hubai, Tamás Csikvari, Peter |
| author_sort | Abért, Miklós |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T09:47:58Z |
| format | Article |
| id | mit-1721.1/104881 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:47:58Z |
| publishDate | 2016 |
| publisher | Springer US |
| record_format | dspace |
| spelling | mit-1721.1/1048812022-09-30T16:56:58Z Matching Measure, Benjamini–Schramm Convergence and the Monomer–Dimer Free Energy Abért, Miklós Hubai, Tamás Csikvari, Peter Massachusetts Institute of Technology. Department of Mathematics Csikvari, Peter 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. Alfréd Rényi Institute of Mathematics. “Lendület” Groups and Graphs Research Group National Science Foundation (U.S.) (Grant DMS-1500219) 2016-10-20T16:57:10Z 2016-10-20T16:57:10Z 2015-07 2015-01 2016-08-18T15:44:41Z Article http://purl.org/eprint/type/JournalArticle 0022-4715 1572-9613 http://hdl.handle.net/1721.1/104881 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. https://orcid.org/0000-0002-1594-9206 en http://dx.doi.org/10.1007/s10955-015-1309-7 Journal of Statistical Physics 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. Springer Science+Business Media New York application/pdf Springer US Springer US |
| spellingShingle | Abért, Miklós Hubai, Tamás Csikvari, Peter Matching Measure, Benjamini–Schramm Convergence and the Monomer–Dimer Free Energy |
| title | Matching Measure, Benjamini–Schramm Convergence and the Monomer–Dimer Free Energy |
| title_full | Matching Measure, Benjamini–Schramm Convergence and the Monomer–Dimer Free Energy |
| title_fullStr | Matching Measure, Benjamini–Schramm Convergence and the Monomer–Dimer Free Energy |
| title_full_unstemmed | Matching Measure, Benjamini–Schramm Convergence and the Monomer–Dimer Free Energy |
| title_short | Matching Measure, Benjamini–Schramm Convergence and the Monomer–Dimer Free Energy |
| title_sort | matching measure benjamini schramm convergence and the monomer dimer free energy |
| url | http://hdl.handle.net/1721.1/104881 https://orcid.org/0000-0002-1594-9206 |
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