I'm looking at "Exact eigenvalues of the Ising Hamiltonian in one-,
two- and three-dimensions in the absence of
a magnetic field" paper by Dixon et al (http://yaroslavvb.com/papers/
dixon-exact.pdf)

They define Hamiltonian for 0 magnetic field as
H=-J Sum_{i,j} S_i S_j, where sum is taken over all the edges in the
model, and S_i indicates spin at position i (I'm assuming it takes
values 1 and -1)

Then they talk about "spectrum of the Hamiltonian". When Hamiltonian
is defined in this way, what is the meaning of the spectrum? (ie, does
it have physical interpretation?)