A Renormalisation Group Method. IV. Stability Analysis

This paper is the fourth in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. The third paper in the series presents a perturbative analysis of a supersymmetric field theory which represents the...

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Bibliographic Details
Published in:Journal of statistical physics 2015-05, Vol.159 (3), p.530-588
Main Authors: Brydges, David C., Slade, Gordon
Format: Article
Language:English
Subjects:
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Summary:This paper is the fourth in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. The third paper in the series presents a perturbative analysis of a supersymmetric field theory which represents the continuous-time weakly self-avoiding walk on Z d . We now present an analysis of the relevant interaction functional of the supersymmetric field theory, which permits a nonperturbative analysis to be carried out in the critical dimension d = 4 . The results in this paper include: proof of stability of the interaction, estimates which enable control of Gaussian expectations involving both boson and fermion fields, estimates which bound the errors in the perturbative analysis, and a crucial contraction estimate to handle irrelevant directions in the flow of the renormalisation group. These results are essential for the analysis of the general renormalisation group step in the fifth paper in the series.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-014-1166-9