A View of Criticality in the Ising Model Through the Relevance Index

The Relevance Index has been introduced to detect key features of the
organization of complex dynamical systems. It is based upon Shannon entropies
and can be used to identify groups of variables that change in a coordinated fashion,
while they are less integrated with the rest of the system. In previous work, we have
shown that the average Relevance Index attains its maximum at the phase transition
in both Ising model and random Boolean networks. In this contribution we present a
further study on the Ising model, showing that the relevance index is maximized for
large groups of variables at criticality. These results provide further evidence to the
hypothesis that this index is a powerful measure for capturing criticality.