We consider a stochastic process generated by 1-D Ising model with competing interactions and describe all distributions of this process. It is shown that the set of all limit Gibbs measures, i.e. phase diagram, consist of ferromagnetic, anti-ferromagnetic, paramagnetic and modulated phases. Also it is proven that on the set of ferromagnetic phases one can reach the phase transition.
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Nasir Ganikhodjaev (2024) studied this question.
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