Numerical study of the antiferromagnetic Ising model on a hypersphere

We built a model where all spins are in interaction with each other via an antiferromagnetic Ising Hamiltonian. The geometry of such a model is a tetrahedron placed on a hypersphere in spaces of dimensions enclosed between 1 and 9. Due to confinement and to the fact that all spins interact which each other, our spin system exhibit frustration. The temperatures of the observed antiferro-paramagnetic transitions are equal for all space dimensions to one of two given values depending on the parity of the space dimension. Moreover, the order parameter $<m>$, i.e. the magnetization of the system, has been also studied.