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hal-00136101, version 1

Periodic boundary conditions on the pseudosphere

François Sausset () 1, Gilles Tarjus () 1

Abstract: We provide a framework to build periodic boundary conditions on the pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian space of constant negative curvature. Starting from the common case of periodic boundary conditions in the Euclidean plane, we introduce all the needed mathematical notions and sketch a classification of periodic boundary conditions on the hyperbolic plane. We stress the possible applications in statistical mechanics for studying the bulk behavior of physical systems and we illustrate how to implement such periodic boundary conditions in two examples, the dynamics of particles on the pseudosphere and the study of classical spins on hyperbolic lattices.

  • 1:  Laboratoire de Physique Théorique de la Matière Condensée (LPTMC)
  • CNRS : UMR7600 – Université Pierre et Marie Curie (UPMC) - Paris VI
  • Domain : Physics/Condensed Matter/Statistical Mechanics
    Physics/Mathematical Physics
    Mathematics/Mathematical Physics
  • Keywords : statistical physics – pseudosphere – hyperbolic plane – computer simulation – periodic boundary conditions
  • Comment : 29 pages
  • Available versions :  v1 (2007-03-13) v2 (2007-03-13) v3 (2007-10-02)
 
  • hal-00136101, version 1
  • http://hal.archives-ouvertes.fr/hal-00136101
  • oai:hal.archives-ouvertes.fr:hal-00136101
  • From: François Sausset <>
  • Submitted on: Tuesday, 13 March 2007 13:10:26
  • Updated on: Tuesday, 13 March 2007 15:07:16