7,139 research outputs found
Combinatorial Space Tiling
The present article studies combinatorial tilings of Euclidean or spherical
spaces by polytopes, serving two main purposes: first, to survey some of the
main developments in combinatorial space tiling; and second, to highlight some
new and some old open problems in this area.Comment: 16 pages; to appear in "Symmetry: Culture and Science
Different facets of the raise and peel model
The raise and peel model is a one-dimensional stochastic model of a
fluctuating interface with nonlocal interactions. This is an interesting
physical model. It's phase diagram has a massive phase and a gapless phase with
varying critical exponents. At the phase transition point, the model exhibits
conformal invariance which is a space-time symmetry. Also at this point the
model has several other facets which are the connections to associative
algebras, two-dimensional fully packed loop models and combinatorics.Comment: 29 pages 17 figure
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