Brydges D., Dimock J., Hurd T.
A non-Gaussian fixed point for $\phi^4$ in $4-\ep$ dimensions - I
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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.