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Quasistationary trajectories of the mean-field XY Hamiltonian model: A topological perspective

Francisco A. Tamarit* and Germán Maglione†

Daniel A. Stariolo‡

Celia Anteneodo§

  • Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina

  • Departamento de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970, Porto Alegre, Brazil

  • Departamento de Física, Pontifícia Universidade Católica do Rio de Janeiro, Caixa Postal 38071, 22452-970, Rio de Janeiro, Brazil and Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180, Rio de Janeiro, Brazil

  • *Electronic address: tamarit@famaf.unc.edu.ar
  • †Electronic address: maglione@tero.fis.uncor.edu
  • ‡Electronic address: stariolo@if.ufrgs.br
  • §Electronic address: celia@cbpf.br
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Phys. Rev. E 71, 036148 – Published 29 March, 2005

DOI: https://doi.org/10.1103/PhysRevE.71.036148

Abstract

We employ a topological approach to investigate the nature of quasistationary states of the mean-field XY Hamiltonian model. We focus on the quasistationary states reached when the system is initially prepared in a fully magnetized configuration. By means of numerical simulations and analytical considerations, we show that, along the quasistationary trajectories, the system evolves in a manifold of critical points of the potential energy function. Although these critical points are maxima, the large number of directions with marginal stability may be responsible for the slow relaxation dynamics and the trapping of the system in such trajectories.

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Phys. Rev. E 71, 036148– Published 29 March, 2005
  • Received 1 November 2004

© 2005 American Physical Society

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