Critical Ising model on random triangulations of the disk : enumeration and local limits

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dc.contributor University of Helsinki, Department of Mathematics and Statistics en
dc.contributor University of Helsinki, Department of Mathematics and Statistics en
dc.contributor.author Chen, Linxiao
dc.contributor.author Turunen, Joonas
dc.date.accessioned 2020-05-15T16:41:01Z
dc.date.available 2020-05-15T16:41:01Z
dc.date.issued 2020-03
dc.identifier.citation Chen , L & Turunen , J 2020 , ' Critical Ising model on random triangulations of the disk : enumeration and local limits ' , Communications in Mathematical Physics , vol. 374 , no. 3 , pp. 1577-1643 . https://doi.org/10.1007/s00220-019-03672-5 en
dc.identifier.issn 0010-3616
dc.identifier.other PURE: 121893110
dc.identifier.other PURE UUID: 0cca53f6-1df8-4220-811e-39f4b6df9e96
dc.identifier.other ArXiv: http://arxiv.org/abs/1806.06668v2
dc.identifier.other WOS: 000508079000001
dc.identifier.other ORCID: /0000-0001-6430-4765/work/74069177
dc.identifier.uri http://hdl.handle.net/10138/314993
dc.description.abstract We consider Boltzmann random triangulations coupled to the Ising model on their faces, under Dobrushin boundary conditions and at the critical point of the model. The first part of this paper computes explicitly the partition function of this model by solving its Tutte's equation, extending a previous result by Bernardi and Bousquet-Melou (J Combin Theory Ser B 101(5):315-377, 2011) to the model with Dobrushin boundary conditions. We show that the perimeter exponent of the model is 7/3 in contrast to the exponent 5/2 for uniform triangulations. In the second part, we show that the model has a local limit in distribution when the two components of the Dobrushin boundary tend to infinity one after the other. The local limit is constructed explicitly using the peeling process along an Ising interface. Moreover, we show that the main interface in the local limit touches the (infinite) boundary almost surely only finitely many times, a behavior opposite to that of the Bernoulli percolation on uniform maps. Some scaling limits closely related to the perimeters of finite clusters are also obtained. en
dc.format.extent 67
dc.language.iso eng
dc.relation.ispartof Communications in Mathematical Physics
dc.rights en
dc.subject math.PR en
dc.subject math-ph en
dc.subject math.CO en
dc.subject math.MP en
dc.subject 05C80, 60K35, 60K37 en
dc.subject PLANAR LATTICE en
dc.subject EQUATIONS en
dc.subject MAP en
dc.subject 111 Mathematics en
dc.title Critical Ising model on random triangulations of the disk : enumeration and local limits en
dc.type Article
dc.description.version Peer reviewed
dc.identifier.doi https://doi.org/10.1007/s00220-019-03672-5
dc.type.uri info:eu-repo/semantics/other
dc.type.uri info:eu-repo/semantics/publishedVersion
dc.contributor.pbl

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