Thermodynamics from Monte Carlo Hamiltonian
  We construct an effective low-energy Hamiltonian from the classical action via Monte Carlo with importance sampling. We use Monte Carlo (i) to compute matrix elements of the transition amplitude and (ii) to construct stochastically a basis. The MC Hamiltonian allows to obtain energies and wave functions of low-lying states. It allows also to compute thermodynamical observables in some temperature window (starting from temperature zero). We present examples from lattice field theory (Klein-Gordon model). 
L.A. Caron, H. Kr\"oger, G. Melkonyan, X.Q. Luo, K.J.M. Moriarty