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arXiv · hep-th/0206040

CRITICAL (Phi^{4}_{3,ε})

D. C. Brydges·P. K. Mitter·B. Scoppola
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Abstract

The Euclidean $(ϕ^{4})_{3,ε$ model in $R^3$ corresponds to a perturbation by a $ϕ^4$ interaction of a Gaussian measure on scalar fields with a covariance depending on a real parameter $ε$ in the range $0\le ε\le 1$. For $ε=1$ one recovers the covariance of a massless scalar field in $R^3$. For $ε=0$ $ϕ^{4}$ is a marginal interaction. For $0\le ε< 1$ the covariance continues to be Osterwalder-Schrader and pointwise positive. After introducing cutoffs we prove that for $ε> 0$, 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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D. C. Brydges, P. K. Mitter, B. Scoppola. 2002-06-06. CRITICAL (Phi^{4}_{3,ε}). https://doi.org/10.1007/s00220-003-0895-4

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