Characterizing elusive correlation lengths by computable information density

The analysis of computable information density (CID) has recently been introduced as a general approach to quantifying order in equilibrium and non-equilibrium many-body systems, both discrete and continuous, even when the underlying form of order is unknown. The approach has been shown to reliably identify phase transitions, determine their character, and to quantitatively predict certain dynamical critical exponents without prior knowledge of the order parameters. A natural question is whether CID may also inform us on the existence of diverging correlation lengths, and their exponents, in the proximity of phase transitions. We study the CID flow under a renormalization group transformation, and show how this can be exploited to extract correlation lengths and their critical exponents without knowledge of the system's specific correlation functions. To demonstrate the greater generality of the approach, we consider a system for which a simple analysis based on pair-correlation functions cannot detect the diverging correlation length. Hence, with this work, we introduce a new approach for the identification of elusive correlation lengths.