Loewner driving force of the interface in the 2-dimensional Ising system as a chaotic dynamical system

The interfaces in the 2-dimensional (2D) ferromagnetic Ising system below and at the critical temperature T_c were numerically analyzed in the framework of discrete Loewner evolution. We numerically calculated Loewner driving forces corresponding to the interfaces in the 2D Ising system and analyzed them using nonlinear time series analyses. We found that the dynamics of the Loewner driving forces showed chaotic properties wherein their intermittency, sensitivity to initial condition, and autocorrelation change depending on the temperature T of the system. It is notable that while the Loewner driving forces have deterministic properties, they have Gaussian-type probability distributions whose variance increases as T→T_c, indicating that they are examples of the Gaussian chaos. Thus, the obtained Loewner driving forces can be considered a chaotic dynamical system whose bifurcation is dominated by the temperature of the Ising system. This perspective for the dynamical system was discussed in relation to the extension and/or generalization of the stochastic Loewner evolution.