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 Electronic Journal of Probability > Vol. 14 (2009) > Paper 57 open journal systems 


Spontaneous breaking of continuous rotational symmetry in two dimensions

Franz Merkl, Mathematical Institute, University of Munich, Germany
Silke W.W. Rolles, Technical University of Munich, Germany


Abstract
In this article, we consider a simple model in equilibrium statistical mechanics for a two-dimensional crystal without defects. In this model, the local specifications for infinite-volume Gibbs measures are rotationally symmetric. We show that at sufficiently low, but positive temperature, rotational symmetry is spontaneously broken in some infinite-volume Gibbs measures.


Full text: PDF

Pages: 1705-1726

Published on: August 10, 2009
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Electronic Journal of Probability. ISSN: 1083-6489