  Few years ago, application of the mean field Bethe scheme on a given system
was shown to produce a systematic change of the system intrinsic symmetry. For
instance, once applied on a ferromagnet, individual spins are no more
equivalent. Accordingly a new loopwise mean field theory was designed to both
go beyond the one site Weiss approach and yet preserve the initial Hamitonian
symmetry. This loopwise scheme is applied here to solve the Triangular
Antiferromagnetic Ising model. It is found to yield Wannier's exact result of
no ordering at non-zero temperature. No adjustable parameter is used.
Simultaneously a non-zero critical temperature is obtained for the Triangular
Ising Ferromagnet. This simple mean field scheme opens a new way to tackle
random systems.
