Two-dimensional random tilings of large codimension: new progress
Abstract
Two-dimensional random tilings of rhombi can be seen as projections of two-dimensional membranes embedded in hypercubic lattices of higher dimensional spaces. Here, we consider tilings projected from a -dimensional space. We study the limiting case, when the quantity , and therefore the number of different species of tiles, become large. We had previously demonstrated [ICQ6] that, in this limit, the thermodynamic properties of the tiling become independent of the boundary conditions. The exact value of the limiting entropy and finite corrections remain open questions. Here, we develop a mean-field theory, which uses an iterative description of the tilings based on an analogy with avoiding oriented walks on a random tiling. We compare the quantities so-obtained with numerical calculations. We also discuss the role of spatial correlations.
Cite
@article{arxiv.cond-mat/9912275,
title = {Two-dimensional random tilings of large codimension: new progress},
author = {N. Destainville and M. Widom and R. Mosseri and F. Bailly},
journal= {arXiv preprint arXiv:cond-mat/9912275},
year = {2016}
}
Comments
Proceedings of the 7th International Conference on Quasicrystals (ICQ7, Stuttgart), 4 pages, 4 figures