Conformal Invariance of Boundary Touching Loops of FK Ising Model

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dc.contributor.author Kemppainen, Antti
dc.contributor.author Smirnov, Stanislav
dc.date.accessioned 2019-06-26T12:01:01Z
dc.date.available 2019-06-26T12:01:01Z
dc.date.issued 2019-07
dc.identifier.citation Kemppainen , A & Smirnov , S 2019 , ' Conformal Invariance of Boundary Touching Loops of FK Ising Model ' , Communications in Mathematical Physics , vol. 369 , no. 1 , pp. 49-98 . https://doi.org/10.1007/s00220-019-03437-0
dc.identifier.other PURE: 58539440
dc.identifier.other PURE UUID: 9f6ab191-6286-4c80-b9a9-45947ec9ad6e
dc.identifier.other WOS: 000470309100002
dc.identifier.other ORCID: /0000-0003-4483-8799/work/58956432
dc.identifier.uri http://hdl.handle.net/10138/303496
dc.description.abstract In this article we show the convergence of a loop ensemble of interfaces in the FK Ising model at criticality, as the lattice mesh tends to zero, to a unique conformally invariant scaling limit. The discrete loop ensemble is described by a canonical tree glued from the interfaces, which then is shown to converge to a tree of branching SLEs. The loop ensemble contains unboundedly many loops and hence our result describes the joint law of infinitely many loops in terms of SLE type processes, and the result gives the full scaling limit of the FK Ising model in the sense of random geometry of the interfaces. Some other results in this article are convergence of the exploration process of the loop ensemble (or the branch of the exploration tree) to SLE(κ,κ−6), κ=16/3, and convergence of a generalization of this process for 4 marked points to SLE[κ,Z], κ=16/3, where Z refers to a partition function. The latter SLE process is a process that can't be written as a SLE(κ,ρ1,ρ2,…) process, which are the most commonly considered generalizations of SLEs. en
dc.format.extent 50
dc.language.iso eng
dc.relation.ispartof Communications in Mathematical Physics
dc.rights cc_by
dc.rights.uri info:eu-repo/semantics/openAccess
dc.subject 111 Mathematics
dc.subject CRITICAL PERCOLATION
dc.title Conformal Invariance of Boundary Touching Loops of FK Ising Model en
dc.type Article
dc.contributor.organization Department of Mathematics and Statistics
dc.description.reviewstatus Peer reviewed
dc.relation.doi https://doi.org/10.1007/s00220-019-03437-0
dc.relation.issn 0010-3616
dc.rights.accesslevel openAccess
dc.type.version publishedVersion

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