  Renormalization group limit cycles may be a commonplace for quantum
Hamiltonians requiring renormalization, in contrast to experience to date with
classical models of critical points, where fixed points are far more common. We
discuss the simplest model Hamiltonian identified to date that exhibits a
renormalization group limit cycle. The model is a discrete Hamiltonian with two
coupling constants and a non-perturbative renormalization group that involves
changes in only one of these couplings and is soluble analytically. The
Hamiltonian is the discrete analog to a continuum Hamiltonian previously
proposed by us.
