Phase transitions and marginal ensemble equivalence for freely evolving   flows on a rotating sphere
  The large-scale circulation of planetary atmospheres like that of the Earth is traditionally thought of in a dynamical framework. Here, we apply the statistical mechanics theory of turbulent flows to a simplified model of the global atmosphere, the quasi-geostrophic model, leading to non-trivial equilibria. Depending on a few global parameters, the structure of the flow may be either a solid-body rotation (zonal flow) or a dipole. A second order phase transition occurs between these two phases, with associated spontaneous symmetry-breaking in the dipole phase. This model allows us to go beyond the general theory of marginal ensemble equivalence through the notion of Goldstone modes. 
Corentin Herbert, B\'ereng\`ere Dubrulle, Pierre-Henri Chavanis and   Didier Paillard
physics.flu-dyn cond-mat.stat-mech physics.ao-ph