Entropy of Folding of the Triangular Lattice
arXiv:cond-mat/9402058 · doi:10.1209/0295-5075/26/6/010
Abstract
The problem of counting the different ways of folding the planar triangular lattice is shown to be equivalent to that of counting the possible 3-colorings of its bonds, a dual version of the 3-coloring problem of the hexagonal lattice solved by Baxter. The folding entropy Log q per triangle is thus given by Baxter's formula q=sqrt(3)(Gamma[1/3])^(3/2)/2pi =1.2087...
9 pages, harvmac, epsf, uuencoded, 5 figures included, Saclay preprint T/94018
Cited by in corpus (29)
- The Statistical Mechanics of Membranes
- Operator Spectrum and Exact Exponents of the Fully Packed Loop Model
- Geometric effects on T-breaking in p+ip and d+id superconductors
- Folding Transition of the Triangular Lattice
- An Iterative Solution of the Three-colour Problem on a Random Lattice
- Hermitian Matrix Model with Plaquette Interaction
- Dynamical obstruction in a constrained system and its realization in lattices of superconducting devices
- Coloring Random Triangulations
- Folding transitions of the triangular lattice with defects
- Geometrically constrained statistical systems on regular and random lattices: From folding to meanders
- Three-dimensional Folding of the Triangular Lattice
- Folding transition of the triangular lattice in a discrete three--dimensional space
- Folding of the triangular lattice in a discrete three-dimensional space: Density-matrix-renormalization-group study
- Fully Packed O(n=1) Model on Random Eulerian Triangulations
- Exact Solution of the Three-color Problem on a Random Lattice
- Folding of the Triangular Lattice with Quenched Random Bending Rigidity
- Folds in 2D String Theories
- Geometrical Folding Transitions of the Triangular Lattice in the Face-Centred Cubic Lattice
- Folding the Square-Diagonal Lattice
- Hamiltonian Cycles on Random Eulerian Triangulations
- Crumpling transition of the discrete planar folding in the negative-bending-rigidity regime
- Exactly solvable flat-foldable quadrilateral origami tilings
- Folding Transitions of the Square-Diagonal Lattice
- Folding of the triangular lattice in a discrete three-dimensional space: Crumpling transitions in the negative-bending-rigidity regime
- Folding pathways to crumpling in thermalized elastic frames
- Folding transitions of the square--diagonal two--dimensional lattice
- Geometrically Constrained Statistical Models on Fixed and Random Lattices: From Hard Squares to Meanders
- Folding of the Triangular Lattice in the FCC Lattice with Quenched Random Spontaneous Curvature
- Gauge symmetry and non-abelian topological sectors in a geometrically constrained model on the honeycomb lattice