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Geometry of Dynamics, Lyapunov Exponents, and Phase Transitions

1997; American Physical Society; Volume: 79; Issue: 22 Linguagem: Inglês

10.1103/physrevlett.79.4361

1092-0145

Lando Caiani, Lapo Casetti, Cecilia Clementi, Marco Pettini,

Chaos control and synchronization

The Hamiltonian dynamics of the classical planar Heisenberg model is numerically investigated in two and three dimensions. In three dimensions peculiar behaviors are found in the temperature dependence of the largest Lyapunov exponent and of other observables related to the geometrization of the dynamics. On the basis of a heuristic argument it is conjectured that the phase transition might correspond to a change in the topology of the manifolds whose geodesics are the motions of the system.