Exact Combinatorial Density of States for the Critical 1D Ising Model
This work provides an exact combinatorial analysis of a 1D antiferromagnetic Ising model at its critical point (B/J=2). It proves that ground-state degeneracies follow Fibonacci and Lucas sequences for open chains and rings. Furthermore, it determines the excitation spectrum using topological defects, showing that the spectrum is quantized in steps related to 2J or 4J, exposing non-trivial spectral gaps near saturation.