Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-06-11
Phys.Rev.E57:3886-3899,1998
Physics
High Energy Physics
High Energy Physics - Theory
REVTeX, 15 PostScript figures, published version
Scientific paper
10.1103/PhysRevE.57.3886
We perform a microcanonical study of classical lattice phi^4 field models in 3 dimensions with O(n) symmetries. The Hamiltonian flows associated to these systems that undergo a second order phase transition in the thermodynamic limit are here investigated. The microscopic Hamiltonian dynamics neatly reveals the presence of a phase transition through the time averages of conventional thermodynamical observables. Moreover, peculiar behaviors of the largest Lyapunov exponents at the transition point are observed. A Riemannian geometrization of Hamiltonian dynamics is then used to introduce other relevant observables, that are measured as functions of both energy density and temperature. On the basis of a simple and abstract geometric model, we suggest that the apparently singular behaviour of these geometric observables might probe a major topological change of the manifolds whose geodesics are the natural motions.
Caiani Lando
Casetti Lapo
Clementi Cecilia
Gatto Raoul
Pettini Giulio
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