02-273 D. C. Brydges, P. K. Mitter, B. Scoppola

CRITICAL $({\bf\Phi}^{4})_{3,\>\epsilon}$ (126K, plain Tex) Jun 19, 02

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Abstract. The Euclidean $(\phi^{4})_{3,\>\epsilon}$ model in ${\bf R}^3$ corresponds to a perturbation by a $\phi^4$ interaction of a Gaussian measure on scalar fields with a covariance depending on a real parameter $\e$ in the range $0\le \e \le 1$. For $\e =1$ one recovers the covariance of a massless scalar field in ${\bf R}^3$. For $\e =0$ $\phi^{4}$ is a marginal interaction. For $0\le \e < 1$ the covariance continues to be Osterwalder-Schrader and pointwise positive. After introducing cutoffs we prove that for $\e > 0$, 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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