A lattice model with Fibonacci degree of degeneracy

In this paper, we explore two different methods of finding the degrees of degeneracy for lattice model systems, specifically constructing one with a Fibonacci degree of degeneracy. We also calculate the number of ground states per site as the golden ratio $(\phi )$ for the system that we constructed and extend our results to systems with $k-$Step Fibonacci degrees of degeneracy. Finally, I end with a few open questions that we may examine for future works.