  We revisit the cluster expansion for Ising lattice gauge theory on
$\mathbb{Z}^m, \, m \ge 3,$ with Wilson action, at a fixed inverse temperature
\( \beta\) in the low-temperature regime. We prove existence and analyticity of
the infinite volume limit of the free energy and compute the first few terms in
its expansion in powers of $e^{-\beta}$. We further analyze Wilson loop
expectations and derive an estimate that shows how the lattice scale geometry
of a loop is reflected in the large $\beta$ asymptotic expansion. Specializing
to axis parallel rectangular loops $\gamma_{T,R}$ with side-lengths $T$ and
$R$, we consider the limiting function
  $$
  V_\beta(R) := \lim_{T \to \infty} - \frac{1}{T} \log \, \langle
W_{\gamma_{T,R}} \rangle_\beta,
  $$
  known as the static quark potential in the physics literature. We verify
existence of the limit (with an estimate on the convergence rate) and compute
the first few terms in the expansion in powers of $e^{-\beta}$. As a
consequence, a strong version of the perimeter law follows. We also treat $-
\log \, \langle W_{\gamma_{T,R}} \rangle_\beta / (T+R)$ as $T, R$ tend to
infinity simultaneously and give analogous estimates.
