The Pierre Weiss and Bethe-Peierls mean-field approximations are implemented for the ferromagnetic Ising model, with emphasis in the spatial fluctuations of the localized magnetic moments. Although in the Bethe-Peierls approximation we do not have a single-particle Hamiltonian, we present a simple way to obtain the mean energy of the lattice using the spin-spin correlation function. We also compare the next-nearest neighbor spin-spin correlation calculated in both mean-field approximations with the exact result for the two-dimensional lattice of 1/2 spin. This comparison shows clearly the supremacy of the Bethe-Peierls method over the Pierre Weiss one.
mean-field; Bethe-Peierls; Ising
