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Lattice Gauge Theory and a Random-Medium Ising Model

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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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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.


The work is supported by Ministry of Science and Higher Education of the Russian Federation, agreement N075-15-2019-1619.

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Correspondence to Mikhail Skopenkov.

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Dedicated to the last real scientists, brave to face real difficulties, not sweeping them under the rug.

The work is supported by Ministry of Science and Higher Education of the Russian Federation, agreement N075-15-2019-1619.

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Skopenkov, M. Lattice Gauge Theory and a Random-Medium Ising Model. Math Phys Anal Geom 25, 18 (2022).

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