CRITICAL (Phi^{4}_{3,\epsilon})

The Euclidean $(\phi^{4})_{3,\epsilon$ model in $R^3$ corresponds to a perturbation by a $\phi^4$ interaction of a Gaussian measure on scalar fields with a covariance depending on a real parameter $\epsilon$ in the range $0\le \epsilon \le 1$. For $\epsilon =1$ one recovers the covariance of a massl...

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Bibliographic Details
Published in:Communications in mathematical physics 2003-09, Vol.240 (1-2), p.281-327
Main Authors: Brydges, D. C., Mitter, P. K., Scoppola, B.
Format: Article
Language:English
Subjects:
Mathematical Physics
Mathematics
Physics
Online Access:Get full text
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Summary:The Euclidean $(\phi^{4})_{3,\epsilon$ model in $R^3$ corresponds to a perturbation by a $\phi^4$ interaction of a Gaussian measure on scalar fields with a covariance depending on a real parameter $\epsilon$ in the range $0\le \epsilon \le 1$. For $\epsilon =1$ one recovers the covariance of a massless scalar field in $R^3$. For $\epsilon =0$ $\phi^{4}$ is a marginal interaction. For $0\le \epsilon < 1$ the covariance continues to be Osterwalder-Schrader and pointwise positive. After introducing cutoffs we prove that for $\epsilon > 0$, sufficiently small, there exists a non-gaussian fixed point (with one unstable direction) of the Renormalization Group iterations. These iterations converge to the fixed point on its stable (critical) manifold which is constructed.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-003-0895-4