  A powerful existing technique for evaluating statistical mechanical
quantities in two-dimensional Ising models is based on constructing a matrix
representing the nearest neighbor spin couplings and then evaluating the
Pfaffian of the matrix. Utilizing this technique and other more recent
developments in evaluating elements of inverse matrices and exact sampling, a
method and computer code for studying two-dimensional Ising models is
developed. The formulation of this method is convenient and fast for computing
the partition function and spin correlations. It is also useful for exact
sampling, where configurations are directly generated with probability given by
the Boltzmann distribution. These methods apply to Ising model samples with
arbitrary nearest-neighbor couplings and can also be applied to general dimer
models. Example results of computations are described, including comparisons
with analytic results for the ferromagnetic Ising model, and timing information
is provided.
