ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The upper bound for the ultraviolet stability of the two-dimensional cosine interaction ∫Λ:cos αcursive-phiξ:dξ, Λ⊆R2, in finite volume Λ is proven for α2 ∈ [4π,8π[, where the theory has been shown to be superrenormalizable [see, e.g., G. Gallavotti, Rev. Mod. Phys. 57, 471 (1985)]. Ultraviolet stability in this interval was proven previously (F. Nicolò, J. Renn, and A.Steinmann, "On the massive sine–Gordon equation in all regions of collapse,'' preprint II Università di Roma, 1985). Here we give a second proof using renormalization group methods based on a multiscale decomposition of the field by showing that the large fluctuations may be controlled by their small probability. The method essentially follows the one given by Nicolò [F. Nicolò, Commun. Math. Phys. 88, 681 (1983)] for α2 ∈ [4π, (32)/(5) π[.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.527054
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