A comparison between the two-dimensional and three-dimensional lattices

By using a new Hamiltonian of interaction we have calculated the interaction energy for two-dimensional and three-dimensional lattices, We present also, approximate analytical formulae and the analytical formulae for the constant of the elastic force. The obtained results show that in the three-dimensional space, the two-dimensional lattice has the lattice constant and the cohesive energy which are smaller than that of the three-dimensional lattice. For appropriate values of the coupling constants, the two-dimensional lattice in a two-dimensional space has both the lattice constant and the cohesive energy, larger than that of the two-dimensional lattice in a three-dimensional space; this means that if there is a two-dimensional space in the Universe, this should be thinner than the three-dimensional space, while the interaction forces should be stronger. On the other hand, if the coupling constant in the two-dimensional lattice in the two-dimensional space is close to zero, the cohesive energy should be comparable with the cohesive energy from three-dimensional space but this two-dimensional space does not emit but absorbs radiation.