The bounded eight-vertex model

Authors:
Kari Eloranta
Affiliations:
Institute of Mathematics, Helsinki University of Technology, FIN-02015 HUT, Finland
Venue:
Theoretical Computer Science - Special issue: Tilings of the plane
Year:
2003

Citing 5
Cited 0

Tilings and patterns

Tilings and patterns
Tiling with Polyominoes and Combinatorial Group Theory

Journal of Combinatorial Theory Series A
Conway's tiling groups

American Mathematical Monthly
Cellular automata for contour dynamics

Physica D
Markov chain algorithms for planar lattice structures

FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

The bounded version of the eight-vertex model of Statistical Mechanics is investigated. We study square, diamond and general finite domains on the square lattice and give exact characterizations to legal boundary conditions and number of fill-ins. The sets of legal configurations with a given boundary turn out always to have the graph topology of a hypercube with a particularly simple edge action. This enables a simple probabilistic description of the configurations as well as an efficient configuration generation using a cellular automaton. Finally, by invoking height functions we study restricted edge action which leads to ice-model as well as to lesser know vertex models, some subsets of the eight-vertex model, some not.