Synergy as a warning sign of transitions: the case of the two-dimensional Ising model

We consider the formalism of information decomposition of target effects from multi-source interactions, i.e. the problem of defining unique, redundant (or shared), and synergistic (or complementary) components of the information that a set of source variables provides about a target, and apply it to the two-dimensional Ising model as a paradigm of a critically transitioning system. We show that the physical quantity that reveals an upcoming transition is the synergy, which peaks in the disordered phase, while the redundancy reaches its maximum at the critical temperature. With respect to previous literature, we show that such reliable marker of an impending dynamical change, the synergy, can be identified considering as few as three variables, and that lagged correlations are not necessary to this scope. Our results provide a conceptual background for the investigation of a variety of systems prone to crisis, like financial markets, social media, or epileptic seizures.

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