  We present a new approach to a classical problem in statistical physics:
estimating the partition function and other thermodynamic quantities of the
ferromagnetic Ising model. Markov chain Monte Carlo methods for this problem
have been well-studied, although an algorithm that is truly practical remains
elusive. Our approach takes advantage of the fact that, for a fixed bond
strength, studying the ferromagnetic Ising model is a question of counting
particular subgraphs of a given graph. We combine graph theory and heuristic
sampling to determine coefficients that are independent of temperature and
that, once obtained, can be used to determine the partition function and to
compute physical quantities such as mean energy, mean magnetic moment, specific
heat, and magnetic susceptibility.
