D. C. Brydges, P. K. Mitter, B. Scoppola
CRITICAL $({\bf\Phi}^{4})_{3,\>\epsilon}$
(126K, plain Tex)

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.