Periodic boundary conditions on the pseudosphere

Details Periodic boundary conditions on the pseudosphere Periodic boundary conditions on the pseudosphere

2007-03-13

arxiv.org/abs/cond-mat/0703326v2

J.PHys.A40:12873-12899,2007

Physics

Condensed Matter

Statistical Mechanics

30 pages, minor corrections, accepted to J. Phys. A

Scientific paper

10.1088/1751-8113/40/43/004

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.

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