  Bethe approximation is shown to violate Bravais lattices translational
invariance. A new scheme is then presented which goes over the one-site Weiss
model yet preserving initial lattice symmetry. A mapping to a one-dimensional
finite closed chain in an external field is obtained. Lattice topology
determines the chain size. Using recent results in percolation, lattice
connectivity between chains is argued to be $(q(d-1)-2)/(d)$ where $q$ is the
coordination number and $d$ is the space dimension. A new self-consistent
mean-field equation of state is derived. Critical temperatures are thus
calculated for a large variety of lattices and dimensions. Results are within a
few percent of exact estimates. Moreover onset of phase transitions is found to
occur in the range $(d-1)q> 2$. For the Ising hypercube it yields the Golden
number limit $d > (1+\sqrt 5)/(2)$.
