  Numerical methods are used to examine the thermodynamic characteristics of
the two-dimensional Ising model as a function of the number of spins N.
Onsager's solution is generalized to a finite-size lattice, and experimentally
validated analytical expressions for the free energy and its derivatives are
computed. The heat capacity at the critical point is shown to grow
logarithmically with N. Due to the finite extent of the system the critical
temperature can only be determined to some accuracy.
