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Height representation of XOR-Ising loops via bipartite dimers

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Height representation of XOR-Ising loops via bipartite dimers
2.	Creator	Author's name, affiliation, country	Cédric Boutillier; UPMC; France
2.	Creator	Author's name, affiliation, country	Béatrice de Tilière; UPMC; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Ising model, bipartite dimer model, height function, homology theory
3.	Subject	Subject classification	52C20; 55N33; 60K35; 82B20; 82B23
4.	Description	Abstract	The XOR-Ising model on a graph consists of random spin configurations on vertices of the graph obtained by taking the product at each vertex of the spins of two independent Ising models. In this paper, we explicitly relate loop configurations of the XOR-Ising model and those of a dimer model living on a decorated, bipartite version of the Ising graph. This result is proved for graphs embedded in compact surfaces of genus $g$. Using this fact, we then prove that XOR-Ising loops have the same law as level lines of the height function of this bipartite dimer model. At criticality, the height function is known to converge weakly in distribution to $\frac{1}{\sqrt{\pi}}$ a Gaussian free field. As a consequence, results of this paper shed a light on the occurrence of the Gaussian free field in the XOR-Ising model. In particular, they provide a step forward in the solution of Wilson's conjecture, stating that the scaling limit of XOR-Ising loops are level lines of the Gaussian free field.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	ANR
7.	Date	(YYYY-MM-DD)	2014-09-04
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/2449
10.	Identifier	Digital Object Identifier	10.1214/EJP.v19-2449
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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