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Investigating critical systems via the distribution of correlation lengths

We introduce a novel approach to study the critical behavior of equilibrium and non-equilibrium systems which is based on the concept of an instantaneous correlation length. We analyze in detail two classical statistical mechanical systems: the XY model and the Ising model, and one of the prototype models of Self-Organized Criticality: the forest fire model (FFM). The proposed method can both capture the critical behavior of the XY model and the Ising model and discriminate between the nature of the phase transition in the two scenarios. When applied to the FFM, it gives surprising results, suggesting that the model could be critical despite displaying broken scaling in the distribution of cluster sizes.