  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.
