Geometry of Dynamics, Lyapunov Exponents, and Phase Transitions

Lando Caiani, Lapo Casetti, Cecilia Clementi, and Marco Pettini
Phys. Rev. Lett. 79, 4361 – Published 1 December 1997
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Abstract

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.

  • Received 6 February 1997

DOI:https://doi.org/10.1103/PhysRevLett.79.4361

©1997 American Physical Society

Authors & Affiliations

Lando Caiani1, Lapo Casetti2, Cecilia Clementi1, and Marco Pettini3

  • 1International School for Advanced Studies (SISSA/ISAS), via Beirut 2-4, 34014 Trieste, Italy
  • 2Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
  • 3Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, 50125 Firenze, Italy

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Issue

Vol. 79, Iss. 22 — 1 December 1997

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