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The critical temperature for the Ising model on planar doubly periodic graphs


 
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1. Title Title of document The critical temperature for the Ising model on planar doubly periodic graphs
 
2. Creator Author's name, affiliation, country David Cimasoni; Université de Genève; Switzerland
 
2. Creator Author's name, affiliation, country Hugo Duminil-Copin; Université de Genève; Switzerland
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Ising model;critical temperature;weighted periodic graph;Kac-Ward matrices;Harnack curves
 
3. Subject Subject classification 82B20
 
4. Description Abstract We provide a simple characterization of the critical temperature for the Ising model on an arbitrary planar doubly periodic weighted graph. More precisely, the critical inverse temperature $\beta$ for a graph $G$ with coupling constants $(J_e)_{e\in E(G)}$ is obtained as the unique solution of an algebraic equation in the variables $(\tanh(\beta J_e))_{e\in E(G)}$. This is achieved by studying the high-temperature expansion of the model using Kac-Ward matrices.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2013-03-28
 
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/2352
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2352
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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