Information Theoretic Characterization of Critical Phenomena in the Ising Model and Flocking Models

The Ising Model, with its known analytical solutions in one and two dimensions, has been used as a prototypical case study for analyzing critical phenomena and phase transitions. Information Theory has been foundational in analyzing the regularity and patterns contained within random processes, exposing the Informational Architecture instantiated in the underlying physical system. In this work we characterize aspects of the informational architecture of the Ising model on the square lattice using multiple measures, including configurational entropy, configurational complexity, and transfer entropy. Their extremal behavior is compared and contrasted with well understood critical behavior in the Ising model as well as Viscek's flocking model. These results strengthen the foundation for understanding how criticality affects information storage and processing in systems that may not have a clear cut order parameter.