Functional Differential Equations for the Free Energy and the Effective   Energy in the Broken-Symmetry Phase of phi^4-Theory and Their Recursive   Graphical Solution
  Extending recent work on QED and the symmetric phase of the euclidean multicomponent scalar \phi^4-theory, we construct the vacuum diagrams of the free energy and the effective energy in the ordered phase of \phi^4-theory. By regarding them as functionals of the free correlation function and the interaction vertices, we graphically solve nonlinear functional differential equations, obtaining loop by loop all connected and one-particle irreducible vacuum diagrams with their proper weights. 
A. Pelster, H. Kleinert