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In a previous work, the n-vicinity method for approximate calculation of thepartition function of a spin system was proposed. The equation of state wasobtained in the most general form. In the present paper, we analyze theapplicability of this method for the Ising model on a D-dimensional cubiclattice. The equation of state is solved for an arbitrary dimension D and thebehavior of the free energy is analyzed. As expected, for large dimensions (D >2) the system demonstrates a phase transition of the second kind. In this case,we obtain an analytical expression for the critical value of the inversetemperature. When 2 < D < 8 this expression is in a very good agreement withthe results of computer simulations. In the case of small dimensions (D < 3),there is a noticeable discrepancy with the known exact results.

Applicability of n-vicinity method for calculation of free energy of Ising model