Phase transitions and Lyapunov characteristic exponents.

We present a molecular-dynamics simulation of a two-dimensional system of coupled rotators [O(2) planar Heisenberg model]. We observe that if the maximal characteristic Lyapunov exponent for the system is plotted versus the temperature, a clear-cut ``knee'' appears precisely in correspondence with the Kosterlitz-Thouless transition temperature. A new order parameter is therefore available which reflects the marked change in the stochasticity properties of the motion of the system as the temperature is varied in the vicinity of the critical temperature.