ABSTRACT
The Gaussian fixed point becomes unstable for
d < 4. In order to search for a stable fixed point for d = 3,
we can no longer regard u as small, and the task of p e r -
forming (7.3) becomes difficult. Fortunately, we can still
learn a great deal about the stable fixed point by studying
the RG for d very close to 4. It turns out that the stable
fixed point lies very close to i f d is less than but
very close to 4. One might think that this should be obvi-
ous by continuity. Since the stable fixed point is at
r Q = u = 0 for d ^ 4, it must be close to (0, 0) for
d = 4-e, with small e > 0. Such a v iew is incorrect since
188 THE GAUSSIAN F IX E D P O IN T
'fi the Gaussian fixed point remains a fixed point, a l-
though becoming unstable, for d < 4, There are now two,
not one, fixed points for d < 4. The stable one is new,
and not a continuation of the Gaussian fixed point from
d > 4.
