1997/06/30 by Lando Caiani, Lapo Casetti, Cecilia Clementi +4 · 57 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Geodesic #Geometry #Hamiltonian (control theory) #Homogeneous space #Lattice (music) #Mathematical physics #Mathematics #Observable #Phase transition #Physics #Protein Structure and Dynamics #Quantum chaos and dynamical systems #Quantum mechanics #Statistical physics #Theoretical and Computational Physics #chao-dyn #cond-mat.stat-mech #hep-th #nlin.CD
paper · pdf · doi:10.1103/physreve.57.3886
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 57(4), 3886-3899 (American Physical Society) · REVTeX, 15 PostScript figures, published version
openalex publication_date 1998/04/01 · arxiv created 1998/04/21 · arxiv updated 2011/07/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We perform a microcanonical study of classical lattice \ensuremathφ4 field models in three dimensions with O(n) symmetries. The Hamiltonian flows associated with these systems that undergo a second-order phase transition in the thermodynamic limit are investigated here. 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 Lyapounov exponents at the transition point are observed. A Riemannian geometrization of Hamiltonian dynamics is then used to introduce other relevant observables, which 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 behavior of these geometric observables might probe a major topological change of the manifolds whose geodesics are the natural motions.