It is pointed out that renormalization may arise not only from the fluctuations but from collective phenomena, too. In a more technical terms, the saddle point of the blocking transformations may generate a nontrivial renormalization group flow.

The spontaneous symmetry breaking in the phi4 model generates the spinodal instability and nontrivial saddle points for the blocking as the cutoff is lowered in the Euclidean momentum space. The generalization of the infinitezimal renormalization group equation is presented to take these saddle points in account on the tree level. By keeping the plane waves as saddle points the resulting renormalized action is found to be flat in the unstable region. This reproduces the Maxwell cut when the cutoff reaches the infrared end point. The degeneracy of the effective action can be shown analytically for arbitrary saddle points by relying on the continuity of the renormalization group flow.

These results can be extended for real time and might serve as the starting point for an alternative description of noneqilibrium dynamics.

Further details: