Thanks for the hints. I'm still confused because I see places use "Ising model Hamiltonian" to denote a a function that gives the energy of a configuration, and what does it mean to find eigenstates of the energy function?
For instance first equation in page below seems to be a function that counts the number of aligned spins
http://www.nyu.edu/classes/tuckerman/stat.mech/lectures/lecture_26/node2.html
Also equation 31 in
http://arxiv.org/abs/cond-mat/0010392v1 also seems to be a function that gives the energy of a configuration. Then the author talks about finding the spectrum of H, but again, how can you find a spectrum of a function that has different range and domain?