Lattice Gauge Theory and a Random-Medium Ising Model

Mikhail Skopenkov

doi:10.1007/s11040-022-09430-9

Lattice Gauge Theory and a Random-Medium Ising Model

Mikhail Skopenkov

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

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Abstract

We study linearization of lattice gauge theory. Linearized theory approximates lattice gauge theory in the same manner as the loop O(n)-model approximates the spin O(n)-model. Under mild assumptions, we show that the expectation of an observable in linearized Abelian gauge theory coincides with the expectation in the Ising model with random edge-weights. We find a similar relation between Yang-Mills theory and 4-state Potts model. For the latter, we introduce a new observable.

Original language	English (US)
Journal	Mathematical Physics Analysis and Geometry
Volume	25
Issue number	3
DOIs	https://doi.org/10.1007/s11040-022-09430-9
State	Published - Jul 6 2022

Bibliographical note

KAUST Repository Item: Exported on 2022-09-14
Acknowledgements: The work is supported by Ministry of Science and Higher Education of the Russian Federation, agreement N075-15-2019-1619.
For the latter conjecture, there have been suggested a proof by K. Izyurov and A. Magazinov, as well as interesting generalizations by M. Fedorov and I. Novikov (private communication) [16 , 17]. The author is grateful to D. Chelkak, H. Duminil-Copin, M. Khristoforov, S. Melikhov, S. Smirnov for useful discussions.

ASJC Scopus subject areas

Mathematical Physics
Geometry and Topology

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10.1007/s11040-022-09430-9

https://repository.kaust.edu.sa/bitstream/10754/679668/1/percolation.pdf

Cite this

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abstract = "We study linearization of lattice gauge theory. Linearized theory approximates lattice gauge theory in the same manner as the loop O(n)-model approximates the spin O(n)-model. Under mild assumptions, we show that the expectation of an observable in linearized Abelian gauge theory coincides with the expectation in the Ising model with random edge-weights. We find a similar relation between Yang-Mills theory and 4-state Potts model. For the latter, we introduce a new observable.",

author = "Mikhail Skopenkov",

note = "KAUST Repository Item: Exported on 2022-09-14 Acknowledgements: The work is supported by Ministry of Science and Higher Education of the Russian Federation, agreement N075-15-2019-1619. For the latter conjecture, there have been suggested a proof by K. Izyurov and A. Magazinov, as well as interesting generalizations by M. Fedorov and I. Novikov (private communication) [16 , 17]. The author is grateful to D. Chelkak, H. Duminil-Copin, M. Khristoforov, S. Melikhov, S. Smirnov for useful discussions.",

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N2 - We study linearization of lattice gauge theory. Linearized theory approximates lattice gauge theory in the same manner as the loop O(n)-model approximates the spin O(n)-model. Under mild assumptions, we show that the expectation of an observable in linearized Abelian gauge theory coincides with the expectation in the Ising model with random edge-weights. We find a similar relation between Yang-Mills theory and 4-state Potts model. For the latter, we introduce a new observable.

AB - We study linearization of lattice gauge theory. Linearized theory approximates lattice gauge theory in the same manner as the loop O(n)-model approximates the spin O(n)-model. Under mild assumptions, we show that the expectation of an observable in linearized Abelian gauge theory coincides with the expectation in the Ising model with random edge-weights. We find a similar relation between Yang-Mills theory and 4-state Potts model. For the latter, we introduce a new observable.

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DO - 10.1007/s11040-022-09430-9

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JO - Mathematical Physics Analysis and Geometry

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ER -

Lattice Gauge Theory and a Random-Medium Ising Model

Abstract

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