Due to insufficient research on the (condensed) matter, we took to ourselves the task of computing the ground state for the Ising model on non-orientable manifolds, this is important because of the recent results regarding broken Lorentz invariance on Condensed matter systems, namely some crystals as seen by Jorge Ranja. By using the Metropolis algorithm, we proved that the ground state for the "simple" case of the Möbius band, contains a spin defect which thermally behaves as a Brownian particle. This is a simple consequence of the breaking of Lorentz Invariance. It can also be seen as the degenerate limit of the Heisenberg model, on a fourth quantized, non-commutative Klein bottle (see Mir Faizal's work). Then, by inserting the resolution of identity, we show that a magnetic field can induce a coherent Brownian wave, which is expected from the Kolmogorov Arnold Moser Theorem. We interpret the results on the light of the theological theory of topological invariants.
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[v1] 2017-02-20 12:09:21
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