Exact Distribution of Energies in the Two-Dimensional Ising Model

The low-temperature series expansion for the partition function of the two-dimensional Ising model on a square lattice can be determined exactly for finite lattices using Kaufman's generalization of Onsager's solution. The exact distribution function for the energy can then be determined from the coefficients of the partition function. This provides an exact solution with which one can compare energy histograms determined in Monte Carlo simulations. This solution should prove useful for detailed studies of statistical and systematic errors in histogram reweighting.