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.
"Spontaneous breaking of continuous rotational symmetry in two dimensions." Electron. J. Probab. 14 1705 - 1726, 2009. https://doi.org/10.1214/EJP.v14-671