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. Laboratoire associé au CNRS (UMR
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