  The universality of renormalization group limit cycle behavior is illustrated
with a simple discrete Hamiltonian model. A non-perturbative renormalization
group equation for the model is soluble analytically at criticality and
exhibits one marginal operator (made necessary by the limit cycle) and an
infinite set of irrelevant operators. Relevant operators are absent. The model
exhibits an infinite series of bound state energy eigenvalues. This infinite
series approaches an exact geometric series as the eigenvalues approach zero -
also a consequence of the limit cycle. Wegner's eigenvalues for irrelevant
operators are calculated generically for all choices of parameters in the
model. We show that Wegner's eigenvalues are independent of location on the
limit cycle, in contrast with Wegner's operators themselves, which vary
depending on their location on the limit cycle. An example is then used to
illustrate numerically how one can tune the initial Hamiltonian to eliminate
the first two irrelevant operators. After tuning, the Hamiltonian's bound state
eigenvalues converge much more quickly than otherwise to an exact geometric
series.
