Large-order behaviour of the 1/N expansion in zero and one dimensions
- 1 June 1979
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 12 (6) , 759-770
- https://doi.org/10.1088/0305-4470/12/6/006
Abstract
The large-order behaviour of the 1/N expansion in the zero- and one-dimensional g phi 4 model is investigated. The one-dimensional N-vector model is also considered. The asymptotic behaviour shows oscillations due to complex instantons. The phase and the amplitude of these leading behaviours are determined theoretically and are compared with the explicit numerical calculations of higher orders. In the one-dimensional g phi 4 model the relevance of the large-N instanton is discussed.Keywords
This publication has 15 references indexed in Scilit:
- Planar diagramsCommunications in Mathematical Physics, 1978
- Perturbation theory at large order. I. TheinteractionPhysical Review D, 1977
- Perturbation theory at large order. II. Role of the vacuum instabilityPhysical Review D, 1977
- Statistical mechanics of one-dimensional Ginzburg-Landau fields: Feynman graph evaluation of the screening approximation (n-1expansion)Journal of Physics A: Mathematical, Nuclear and General, 1974
- Statistical mechanics of zero-dimensional ginzburglandau fields: Accuracy of the screening approximationJournal of Statistical Physics, 1974
- Phase transitions for one and zero dimensional systems with short-range forcesAnnals of Physics, 1974
- Coupled Anharmonic Oscillators. I. Equal-Mass CasePhysical Review D, 1973
- Critical Exponent η up to 1/n2for the Three-Dimensional System with Short-Range InteractionProgress of Theoretical Physics, 1973
- Anharmonic Oscillator. II. A Study of Perturbation Theory in Large OrderPhysical Review D, 1973
- Anharmonic OscillatorPhysical Review B, 1969