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2009 Spontaneous breaking of continuous rotational symmetry in two dimensions
Franz Merkl, Silke Rolles
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Electron. J. Probab. 14: 1705-1726 (2009). DOI: 10.1214/EJP.v14-671


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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Franz Merkl. Silke Rolles. "Spontaneous breaking of continuous rotational symmetry in two dimensions." Electron. J. Probab. 14 1705 - 1726, 2009.


Accepted: 10 August 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1191.60115
MathSciNet: MR2535010
Digital Object Identifier: 10.1214/EJP.v14-671

Primary: 60K35
Secondary: 82B20 , 82B21

Keywords: continuous symmetry , Gibbs measure , rotation , spontaneous symmetry breaking

Vol.14 • 2009
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