Rigorous Probabilistic Analysis of Equilibrium Crystal Shapes
Probability
2011-08-25 v1 Statistical Mechanics
Mathematical Physics
math.MP
Abstract
The rigorous microscopic theory of equilibrium crystal shapes has made enormous progress during the last decade. We review here the main results which have been obtained, both in two and higher dimensions. In particular, we describe how the phenomenological Wulff and Winterbottom constructions can be derived from the microscopic description provided by the equilibrium statistical mechanics of lattice gases. We focus on the main conceptual issues and describe the central ideas of the existing approaches.
Cite
@article{arxiv.math/9911106,
title = {Rigorous Probabilistic Analysis of Equilibrium Crystal Shapes},
author = {T. Bodineau and D. Ioffe and Y. Velenik},
journal= {arXiv preprint arXiv:math/9911106},
year = {2011}
}
Comments
To appear in the March 2000 special issue of Journal of Mathematical Physics on Probabilistic Methods in Statistical Physics