Relevant spontaneous magnetization relations for the triangular and the cubic lattice model

Abstract

The spontaneous magnetization relations for the 2D triangular and the 3D cubic lattices of the Ising model are derived by a new tractable and easily calculable mathematical method. The result obtained for the triangular lattice is compared with the already available result to test and investigate the relevance of the new mathematical method. From this comparison, it is seen that the agreement of our result is almost the same or almost equivalent to the previously obtained exact result. The new approach is, then, applied to the long-standing 3D cubic lattice, and the corresponding expression for the spontaneous magnetism is derived. The relation obtained is compared with the already existing numerical results for the 3D lattice. The essence of the method used in this paper is based on exploiting the main characteristic of the order parameter of a second order phase transition which provides a more direct physical insight into the calculation of the spontaneous magnetization of the Ising model.