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.

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Pages: 1705-1726

Publication Date: August 10, 2009

DOI: 10.1214/EJP.v14-671

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