Spontaneous Symmetry Breaking and Propagating Hydrodynamic Wave in the Critical Region

Hydrodynamics is developed in the critical region of phase transition by noticing that the effect of spontaneous symmetry breaking must fully be taken into account there, where the symmetry breaking appearing locally above the critical temperature T c increases its both coherence length and life time to infinity as temperature T approaches T c . It is predicted that an energy density wave will finally be observed as we approach arbitrarily close to T c from above. In magnets, only the diffusive excitation of local magnetization is expected if the observation takes place during a finite time which is much larger than the life time τ SB of the local symmetry breaking above T c . This situation of observation cannot be realized in the limit T → T c since the life time τ SB diverges in the same limit. On the other hand, if the time needed for the observation is less than the life time τ SB specifically in the critical region, the alternative hydrodynamic excitation to be observed is an energy density wave.