A NEW SCHEME FOR ENUMERATING CONNECTED DIAGRAMS ON THE LATTICE

In this article, a scheme based on recursive generation of connected diagrams is proposed for enumerating the connected diagrams in various expansions for lattice field theories. This scheme is rigorous and general, and can be applied to the analytical methods in various lattice field theories. Some notions and results of the modern graph theory in mathematics are used. As examples, the diagram theoretic factors that occur in the average link energy of the lattice chiral field model and in the external source parameter of the pure lattice gauge field model are calculated. © 1990 American Institute of Physics.