  The Marcu-Fredenhagen ratio is a quantity used in the physics literature to
differentiate between phases in lattice Higgs models. It is defined as the
limit of a ratio of expectations of Wilson line observables as the length of
these lines go to infinity while the parameters of the model are kept fixed. In
this paper, we show that the Marcu-Fredenhagen ratio exists in all predicted
phases of the model, and show that it indeed undergoes a phase transition. In
the Higgs phase of the model we do a more careful analysis of the ratio to
deduce its first order behaviour and also give an upper bound on its rate of
convergence. Finally, we also present a short and concise proof of the
exponential decay of correlations in the Higgs phase.
