Emergent chaos in the verge of phase transitions (2019)
The description of phase transitions on different physical systems is usually done using Yang and Lee theory. In short, it depicts a phase as a region of the space of configurations in which certain quantities, state functions, behave in a similar manner and where they vary smoothly. In this work, an attempt of discovering similar characteristics in quantities describing the dynamical system which arise from Hamilton equations was done. The Lyapunov exponents, Hausdorff dimension and Kolmogorov Sinai entropy gave interesting results. In fact, the macroscopical description of the system using statistical mechanics and the microscopical characterization as a dynamical system seems to coincide and this leads to interesting questions of how this relation could be exploited to diagnose critical behavior in a many-body system.