  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.
