Analytical expressions for a finite-size 2D Ising model

Numerical methods are used to examine the thermodynamic characteristics of the twodimensional 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.