The bounded 19-vertex model
Statistical Mechanics
2017-10-11 v1 Mathematical Physics
math.MP
Abstract
We study the 19-vertex model of Statistical Mechanics in a square with the domain wall boundary condition. Using the minimal set of generating flip actions we build a parametrized dynamic version of the model. For all observed dynamic weight values the equilibrium states exhibit clear limit shapes. Although the model in a way incorporates the 6-vertex model, the reason for the existence of the limit shape is fundamentally more general. We conclude with a further study relating the local path geometry to the macroscopic shape geometry.
Cite
@article{arxiv.1710.03609,
title = {The bounded 19-vertex model},
author = {Kari Eloranta},
journal= {arXiv preprint arXiv:1710.03609},
year = {2017}
}