  In this paper, we study lattice gauge theory on \( \mathbb{Z}^4 \) with
finite Abelian structure group. When the inverse coupling strength is
sufficiently large, we give an upper bound on the decay of correlations of
local functions and compute the leading order term for both the expected value
of the spin at a given plaquette as well as for the two-point correlation
function. Moreover, we give an upper bound on the dependency of the size of the
box on which the model is defined. The results in this paper extend and refine
results by Chatterjee and Borgs.
