Can ‘sub-quantum’ theories based on a background field escape Bell’s no-go theorem ?

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In systems described
by Ising-like Hamiltonians, such as spin-lattices, the Bell Inequality can be
strongly violated. Surprisingly, these systems are both local and
non-superdeterministic. They are local, because 1) they include only local,
near-neighbor interaction, 2) they satisfy, accordingly, the Clauser-Horne
factorability condition, and 3) they can violate the Bell Inequality also in dynamic
Bell experiments. Starting from this result we construct an elementary
hidden-variable model, based on a generalized Ising Hamiltonian, describing the
interaction of the Bell-particles with a stochastic ‘background’ medium. We
suggest that such a model is a simple version of a variety of recently
developed ‘sub-quantum’ theories, by authors as Nelson, Adler, De la Pena,
Cetto, Groessing, Khrennikov, all based on a background field. We investigate
how the model might be turned into a realistic theory. Finally, it appears that
background-based models can be tested and discriminated from quantum mechanics
by a straightforward extension of existing experiments.