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Geometry of dynamics and phase transitions in classical lattice phi^4 theories

Lando Caiani·Lapo Casetti·Cecilia Clementi·Giulio Pettini·Marco Pettini·Raoul Gatto
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Abstract

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.

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Lando Caiani, Lapo Casetti, Cecilia Clementi, Giulio Pettini, Marco Pettini, Raoul Gatto. 1998-04-21. Geometry of dynamics and phase transitions in classical lattice phi^4 theories. https://doi.org/10.1103/physreve.57.3886

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