96-681 Brydges D., Dimock J., Hurd T.

A non-Gaussian fixed point for $\phi^4$ in $4-\ep$ dimensions - I (118K, LaTeX) Dec 18, 96

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Abstract. We consider the $\f ^4$ quantum field theory in four dimensions. The Gaussian part of the measure is modified to simulate $4-\ep$ dimensions where $\ep$ is small and positive. We give a renormalization group analysis for the infrared behavior of the resulting model. We find that the Gaussian fixed point is unstable but that there is a hyperbolic non-Gaussian fixed point a distance $\cO(\ep)$ away. In a neighborhood of this fixed point we construct the stable manifold.

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