  We analize the statistical mechanics of a long-range antiferromagnetic model
defined on a D-dimensional hypercube, both at zero and finite temperatures. The
associated Hamiltonian is derived from a recently proposed complexity measure
of Boolean functions, in the context of neural networks learning processes. We
show that, depending of the value of D, the system either presents a low
temperature antiferromagnetic stable phase or the global antiferromagnetic
order disappears at any temperature. In the last case the ground state is an
infinitely degenerated non-glassy one, composed by two equal size anti-aligned
antiferromagnetic domains. We also present some results for the ferromagnetic
version of the model.
