Summing Feynman Graphs by Monte-Carlo: Planar phi(sup 3)-Theory and Dynamically Triangulated Random Surfaces

摘要

New combinatorial identities are suggested relating the ratio of (n-1)-th and n-th orders of (planar) perturbation expansion for any quantity to some average over the ensemble of all planar graphs of the n-th order. These identities are used for Monte-Carlo calculation of critical exponents gamma /sub str/ (string susceptibility) in planar phi/sup 3/-theory and in the dynamically triangulated random surface (DTRS) model near the convergence circle for various dimensions. In the solvable case D = 1 the exact critical properties of the theory are reproduced numerically. (ERA citation 13:057879)