Information Measures of Complexity Applied to the Ising Model, Poster 44

The objective of this work was to verify the usefulness of the information measures of complexity proposed by Gershenson and Fernandez in 2012. The four measures in question are for emergence, self-organization, complexity,... [ view full abstract ]

The objective of this work was to verify the usefulness of the information measures of complexity proposed by Gershenson and Fernandez in 2012. The four measures in question are for emergence, self-organization, complexity, and homeostasis. Our results agreed with those of Gershenson and Fernandez. We also found evidence that maximum complexity, as they defined, has a correspondence with critical points in both random Boolean networks (RBNs) and the Ising model. We recreated Gershenson and Fernandez’s original RBN experiments presented in their 2012 and 2014 papers and applied their measures to the classical Ising model. Our RBN results found maximum complexity at a connectivity of ~3.0 compared to Gershenson and Fernandez’s maximum complexity at ~2.3. Both findings are in agreement with the expected range of 2 to 3. All measures depicted similar curves to those found by Gershenson and Fernandez. The application of the measures to the Ising model showed that maximum complexity occurred at 2.25 in proximity to the critical temperature, Tc = 2.26.... This suggests that maximum complexity corresponds to critical points and that the information complexity measures could be a useful tool in investigating phase transitions in physical systems. It also provides significant evidence for the usefulness of the proposed information measures of complexity. Future work could entail the application of the complexity measures to other complex systems, investigation of the relationship between Lyapunov exponents and homeostasis, and investigation of the relationship between Gershenson and Fernandez’s information measure of complexity and phase transitions in other physical systems.