  We consider the 4D fixed length lattice Higgs model with Wilson action for
the gauge field and structure group $\mathbb{Z}_n$. We study Wilson line
observables in the strong coupling regime and compute their asymptotic behavior
with error estimates. Our analysis is based on a high-temperature
representation of the lattice Higgs measure combined with Poisson
approximation. We also give a short proof of the folklore result that Wilson
line (and loop) expectations exhibit perimeter law decay whenever the Higgs
field coupling constant is positive.
