Lyapunov instability in the extended XY-model: Equilibrium and nonequilibrium molecular dynamics simulations

The extended XY-model, a classical system of planar rotators with nearest neighbor interaction, is studied with molecular dynamics simulations. This model exhibits a first-order phase transition between a low-temperature phase with algebraic decay of spatial correlations and a high-temperature phase, where the correlations decay exponentially. The nature of this phase transition can be changed from continuous to discontinuous by changing a control parameter for the interaction potential. For both phases full spectra of Lyapunov exponents are computed, and their dependence on the energy of the system is investigated. The maximum Lyapunov exponent is determined over a wide range of temperatures, and is shown to exhibit a maximum at the transition temperature if the transition is discontinuous. Furthermore, the behavior of the system in nonequilibrium steady states is considered, and the coefficient for energy transport is calculated by means of equilibrium (Green-Kubo theory) and nonequilibrium molecular dynamics.