  The Monte Carlo (MC) Hamiltonian is a new stochastic method to solve
many-body problems. The MC Hamiltonian represents an effective Hamiltonian in a
finite energy window. We construct it from the classical action via Monte Carlo
with importance sampling. The MC Hamiltonian yields the energy spectrum and
corresponding wave functions in a low energy window. This allows to compute
thermodynamical observables in a low temperature window. We show the working of
the MC Hamiltonian by an example from lattice field theory (Klein-Gordon
model).
