Entropy and Boundary Conditions in Random Lozenge Tilings
| dc.creator | Destainville, N. | |
| dc.date | 1998-04-06 | |
| dc.date.accessioned | 2026-07-07T03:10:16Z | |
| dc.date.available | 2026-07-07T03:10:16Z | |
| dc.description | The tilings of lozenges in 2 dimensions and of rhomboedra in 3 dimensions are studied when they are constrained by fixed boundary conditions. We establish a link between those conditions and free or periodic boundary ones: the entropy is written as a functional integral which is treated via a saddle-point method. Then we can exhibit the dominant states of the statistical ensemble of tilings and show that they can display a strong structural inhomogeneity caused by the boundary. This inhomogeneity is responsible for a difference of entropy between the studied fixed boundary tilings and free boundary ones. This method uses a representation of tilings by membranes embedded in a higher-dimensional hypercubic lattice. It is illustrated in the case of 60 degree lozenge tilings. | |
| dc.description | 20 pages, LaTeX, 6 figures, submitted to J. Phys. A: Math. Gen | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9804062 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9804062 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/28187 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Entropy and Boundary Conditions in Random Lozenge Tilings | |
| dc.type | text |