  In this note, we provide a unifying framework to investigate the
computational complexity of classical spin models and give the full
classification on spin models in terms of system dimensions, randomness,
external magnetic fields and types of spin coupling. We further discuss about
the implications of NP-complete Hamiltonian models in physics and the
fundamental limitations of all numerical methods imposed by such models. We
conclude by a brief discussion on the picture when quantum computation and
quantum complexity theory are included.
