CRITICAL (Phi^{4}_{3,ε})

Details CRITICAL (Phi^{4}_{3,ε}) CRITICAL (Phi^{4}_{3,ε})

2002-06-05

arxiv.org/abs/hep-th/0206040v2

Commun.Math.Phys. 240 (2003) 281-327

Physics

High Energy Physics

High Energy Physics - Theory

49 pages, plain tex, macros included

Scientific paper

10.1007/s00220-003-0895-4

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.

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