The combinatorial factor method for solving Ising model

In this work, we have used a combinatorial factor to find the thermodynamic properties of the Ising model with any coordination numbers in the presence and absence of magnetic field. In this manner, first, we have introduced a combinatorial factor, then using Lagrange multipliers; the Helmholtz free energy have been minimized and finally we have obtained an exact partition function for each spin for various coordination numbers. This method was applied for simple models and the results are compared with transfer matrix method.