One dimensional spin glasses with potential decay 1/r1+g. Absence of phase transitions and cluster properties
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One-dimensional Ising spin systems interacting via a two-body random potential are considered; a decay with the distance like 1/r1+ε is assumed.
We consider only boundary conditions independent of the random realization of the interactions and prove uniqueness and cluster properties of Gibbs states with probability one.
KeywordsBoundary Condition Neural Network Phase Transition Statistical Physic Complex System
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