Archimedean ice

Kari Eloranta*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

The striking boundary dependency, the Arctic Circle Phenomenon, exhibited in the Ice model on the square lattice extends to other planar set-ups. This can be shown using a dynamical formulation which we present for the Archimedean lattices. Critical connectivity results guarantee that the Ice configurations can be generated using the simplest and most efficient local actions. Height functions are utilized throughout the analysis. On a hexagon with suitable boundary height the cellular automaton dynamics generates highly nontrivial Ice equilibria in the triangular and Kagomé cases. On the remaining Archimedean lattice for which the Ice model can be defined, the 3.4.6.4. lattice, the long range behavior is shown to be completely different due to strictly positive entropy for all boundary conditions.

Original languageEnglish
Pages (from-to)4291-4303
Number of pages13
JournalDISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS: SERIES A
Volume33
Issue number9
DOIs
Publication statusPublished - Sep 2013
MoE publication typeA1 Journal article-refereed

Keywords

  • Archimedean lattice
  • Cellular automaton
  • Ice model
  • Measure of maximal entropy
  • Spatial phase transition
  • Vertex rule

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