<div class="csl-bib-body">
<div class="csl-entry">Lis, M. (2025, July 1). <i>Random Geometric Structures and Statistical Physics</i> [Conference Presentation]. Workshop “Random Geometric Structures and Statistical Physics,” Rom, Italy. http://hdl.handle.net/20.500.12708/225050</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/225050
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dc.description.abstract
We define a new Edwards-Sokal representation of the Ising model using double random currents, and introduce a joint coupling along with a XOR-Ising model and the associated height function. After taking the scaling limit of all discrete structures, we discuss our main result: a natural coupling of the Ising magnetisation field and the Gaussian free field. To the best of our knowledge, the existence of such a coupling was not predicted previously, and extends the bosonization picture for the XOR-Ising model. Moreover, the coupling has a geometric nature and is built via the two-valued sets of the GFF.
We will touch on the main elements of the proof: an FKG property of the relevant percolation model, the resulting RSW theory, and an L^2 approximation scheme for the counting (discrete area) measures on the clusters of the percolation.
As a challenge for the future, we also state related conjectures for the Ashkin-Teller model.
en
dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.language.iso
en
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dc.subject
Ising model
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dc.subject
Gaussian free field
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dc.title
Random Geometric Structures and Statistical Physics
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dc.type
Presentation
en
dc.type
Vortrag
de
dc.relation.grantno
59944 / P 36298
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dc.relation.grantno
F 100200
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dc.type.category
Conference Presentation
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tuw.project.title
Spins, Felder und Schleifen
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tuw.project.title
Diskrete Zufallsstrukturen: Abzählung und Grenzobjekte, Dimer model: dynamics and scaling limits
