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Journal of Pure and Applied Mathematics

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Sigmoid functionization of magnetization in the spin-glass Ising model.

Author(s): Akira Saito*

The magnetization of the spin-glass Ising model can be expressed using a sigmoid function. In the ground state, the magnetization is determined by solving a set of nonlinear simultaneous equations, each corresponding to a magnetization. As the magnetization of the ground state in the spin-glass Ising model constitutes an NPcomplete problem, the P=NP problem can be reformulated as solving these nonlinear simultaneous equations. If practical computation yields result that are feasible, it can be essentially considered as P=NP. Furthermore, all interacting systems in nature can be represented by sigmoid functions, and the ground state can be obtained by solving nonlinear simultaneous equations.


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