  We perform a numerical investigation of the Lyapunov spectra of chaotic
dynamics in lattices of classical spins in the vicinity of second-order
ferromagnetic and antiferromagnetic phase transitions. On the basis of this
investigation, we identify a characteristic of the shape of the Lyapunov
spectra, the "G-index", which exhibits a sharp peak as a function of
temperature at the phase transition, provided the order parameter is capable of
sufficiently strong dynamic fluctuations. As a part of this work, we also
propose a general numerical algorithm for determining the temperature in
many-particle systems, where kinetic energy is not defined.
