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

Lattice gauge theory and a random-medium Ising model