Geometrically constrained statistical systems on regular and random lattices: From folding to meanders

Details Geometrically constrained statistical systems on regular and random lattices: From folding to meanders Geometrically constrained statistical systems on regular and random lattices: From folding to meanders

2005-05-11

arxiv.org/abs/cond-mat/0505293v1

Physics Reports 415 (2005) 1-88

Physics

Condensed Matter

Statistical Mechanics

112 pages, 82 figures, harvmac, mssymb, epsf. Review article

Scientific paper

10.1016/j.physrep.2005.05.001

We review a number a recent advances in the study of two-dimensional statistical models with strong geometrical constraints. These include folding problems of regular and random lattices as well as the famous meander problem of enumerating the topologically inequivalent configurations of a meandering road crossing a straight river through a given number of bridges. All these problems turn out to have reformulations in terms of fully packed loop models allowing for a unified Coulomb gas description of their statistical properties. A number of exact results and physically motivated conjectures are presented in detail, including the remarkable meander configuration exponent alpha=(29+sqrt(145))/12.

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