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

Research output: Contribution to journalReview articlepeer-review

Abstract

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 α = (29 + √145/12.

Original languageEnglish (US)
Pages (from-to)1-88
Number of pages88
JournalPhysics Reports
Volume415
Issue number1
DOIs
StatePublished - Aug 2005
Externally publishedYes

Keywords

  • Coloring
  • Eulerian gravity
  • Folding
  • Fully-packed loops
  • Hamiltonian cycles
  • Meanders

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Fingerprint

Dive into the research topics of 'Geometrically constrained statistical systems on regular and random lattices: From folding to meanders'. Together they form a unique fingerprint.

Cite this