<div class="csl-bib-body">
<div class="csl-entry">Lis, M. (2025, December 6). <i>Zeros of Planar Ising Models via Flat SU(2) Connections</i> [Conference Presentation]. NYU Shanghai Probability Seminar, China. http://hdl.handle.net/20.500.12708/225270</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/225270
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dc.description.abstract
Livine and Bonzom recently proposed a geometric formula for a certain set of complex zeros of the partition function of the Ising model defined on planar graphs Livine and Bonzom (Phys Rev D 111(4):046003, 2025). Remarkably, the zeros depend locally on the geometry of an immersion of the graph in three dimensional Euclidean space (different immersions give rise to different zeros). When restricted to the flat case, the weights become the critical weights on circle patterns Lis (Commun Math Phys 370(2):507–530, 2019).We rigorously prove the formula by geometrically constructing a null eigenvector of the Kac–Ward matrix whose determinant is the squared partition function. The main ingredient of the proof is the realisation that the associated Kac–Ward transition matrix gives rise to an SU(2)
connection on the graph, creating a direct link with rotations in three dimensions. The existence of a null eigenvector turns out to be equivalent to this connection being flat.
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.title
Zeros of Planar Ising Models via Flat SU(2) Connections
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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
