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Simulation reduction of the Ising model to general matchings


 
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1. Title Title of document Simulation reduction of the Ising model to general matchings
 
2. Creator Author's name, affiliation, country Mark L Huber; Claremont McKenna College; United States
 
2. Creator Author's name, affiliation, country Jenny Law; Duke University; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Monte Carlo; simulation reduction; canonical paths; fpras
 
3. Subject Subject classification 60C05; 65C05; 82B20
 
4. Description Abstract A distribution is tractable if it is possible to approximately sample from the distribution in polynomial time. Here the ferromagnetic Ising model with unidrectional magnetic field is shown to be reducible to a standard distribution on matchings that is tractable. This provides an alternate method to the original Jerrum and Sinclair approach to show that the Ising distribution itself is tractable. Previous reductions of the Ising model to perfect matchings on different graphs exist, but these older distributions are not tractable. Also, the older reductions did not consider an external magnetic field, while the new reduction explictly includes such a field. The new reduction also helps to explain why the idea of canonical paths is so useful inapproximately sampling from both problems. In addition, the reduction allows any algorithm for matchings to immediately be applied to the Ising model. For instance, this immediately yields a fully polynomial time approximation scheme for the Ising model on a bounded degree graph with magnetization bounded away from 0, merely by invoking an existing algorithm for matchings.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) National Science Foundation
 
7. Date (YYYY-MM-DD) 2012-04-29
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/1998
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-1998
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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