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Few years ago, application of the mean field Bethe scheme on a given systemwas shown to produce a systematic change of the system intrinsic symmetry. Forinstance, once applied on a ferromagnet, individual spins are no moreequivalent. Accordingly a new loopwise mean field theory was designed to bothgo beyond the one site Weiss approach and yet preserve the initial Hamitoniansymmetry. This loopwise scheme is applied here to solve the TriangularAntiferromagnetic Ising model. It is found to yield Wannier's exact result ofno ordering at non-zero temperature. No adjustable parameter is used.Simultaneously a non-zero critical temperature is obtained for the TriangularIsing Ferromagnet. This simple mean field scheme opens a new way to tacklerandom systems.Comment: 14 pages, 2 figure

Solving the triangular Ising antiferromagnet by simple mean field