Spontaneous breaking of rotational symmetry in the presence of defects
Franz Merkl (University of Munich)
Silke W.W. Rolles (Technical University of Munich)
Abstract
We prove a strong form of spontaneous breaking of rotational symmetry for a simple model of two-dimensional crystals with random defects in thermal equilibrium at low temperature. The defects consist of isolated missing atoms.
Full Text: Download PDF | View PDF online (requires PDF plugin)
Pages: 1-17
Publication Date: December 11, 2014
DOI: 10.1214/EJP.v19-2971
References
- Aizenman, Michael; Jansen, Sabine; Jung, Paul. Symmetry breaking in quasi-1D Coulomb systems. Ann. Henri Poincare 11 (2010), no. 8, 1453-1485. MR2769702
- Aumann, Simon. Spontaneous breaking of rotational symmetry with arbitrary defects and a rigidity estimate, Preprint arXiv:1408.5375 [math.PR], 2014.
- Flatley, Lisa and Theil, Florian. Face-centered cubic crystallization of atomistic configurations, Preprint arXiv:1407.0692 [math.AP], 2014.
- Friesecke, Gero; James, Richard D.; Müller, Stefan. A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. Comm. Pure Appl. Math. 55 (2002), no. 11, 1461-1506. MR1916989
- Gaal, Alexisz Tamas. Long-range order in a hard disk model in statistical mechanics. Electron. Commun. Probab. 19 (2014), no. 9, 9 pp. MR3167882
- Georgii, Hans-Otto. Gibbs measures and phase transitions. Second edition. de Gruyter Studies in Mathematics, 9. Walter de Gruyter & Co., Berlin, 2011. xiv+545 pp. ISBN: 978-3-11-025029-9 MR2807681
- Le Bris, Claude; Lions, Pierre-Louis. From atoms to crystals: a mathematical journey. Bull. Amer. Math. Soc. (N.S.) 42 (2005), no. 3, 291--363 (electronic). MR2149087
- Merkl, Franz; Rolles, Silke W. W. Spontaneous breaking of continuous rotational symmetry in two dimensions. Electron. J. Probab. 14 (2009), no. 57, 1705--1726. MR2535010
- International Union of Crystallography, Online Dictionary of Crystallography, http://reference.iucr.org/dictionary/Crystal, October 2014.
- Richthammer, Thomas. Translation-invariance of two-dimensional Gibbsian point processes. Comm. Math. Phys. 274 (2007), no. 1, 81--122. MR2318849
- Theil, Florian. A proof of crystallization in two dimensions. Comm. Math. Phys. 262 (2006), no. 1, 209--236. MR2200888
This work is licensed under a Creative Commons Attribution 3.0 License.