Modeling thermal fluctuations: phase mixing and percolation

We consider the nonequilibrium dynamics of a real scalar field in a double-well potential. The system is initially prepared in one well and coupled to a thermal bath. Using a simple analytical model, we compute the equilibrium fraction of the total volume in each phase as a function of the parameters of the potential. We also show how complete phase mixing, i.e. symmetry restoration, is related to percolation, which is dynamically driven by domain instability. Our method describes quantitatively recent numerical results, and is applicable to systems in the Ising universality class.