Recursive graphical construction of Feynman diagrams and their weights in Ginzburg–Landau theory

The free energy of the Ginzburg–Landau theory satisfies a nonlinear functional differential equation which is turned into a recursion relation. The latter is solved graphically order by order in the loop expansion to find all connected vacuum diagrams, and their corresponding weights. In this way, we determine the connected vacuum diagrams and their weights up to four loops.