Periodic boundary conditions on the pseudosphere

We provide a framework for building 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 required 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 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.

• Publication year

  2007

• Venue

  Journal of Physics A: Mathematical and Theoretical

• Publication date

  2007-03-13

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1088/1751-8113/40/43/004arXiv cond-mat/0703326
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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