Details of the calculation to O(1n2) of the polarization part and of the vertex function with one 2 insertion are given for an n-component, three-dimensional system with O(n) symmetric, short-ranged interaction. The critical indices « and are deduced and are found to conform to other indices available to the same order. An analysis of how the requirements of exponentiation and universality are fulfilled shows that they are consequences of the fulfillment of a scaling law at the previous order. Cutoff-dependent contributions are seen to split off automatically. With possible higher-order calculations in mind considerable stress is put on the technical side: An apparently novel type of regularization technique allows one to pick up the relevant terms directly and is shown to be connected to a kind of analytic regularization. Graphs with diagonal insertions are calculated from generalized Feynman amplitudes associated with first-order diagrams. Those with vertex insertions, as well as irreducible graphs are handled by an integration technique taken over from conformal invariant field theory. The numerical performance of the 1n expansion is discussed, and an attempt is made to obtain more meaningful numbers from the expansion through various Padé- and Padé-Borel-type resummations. The results are compared with information available from other sources.
ASJC Scopus subject areas
- Condensed Matter Physics