  Applying the Exact Renormalization Group to scalar field theory in Euclidean
space of general (not necessarily integer) dimension, it is proven that the
only fixed-point with vanishing anomalous dimension is the Gaussian one. The
proof requires positivity of the two-point connected correlation function
together with a technical assumption concerning solutions of the flow equation.
The method, in which the representation of the flow equation as a heat equation
plays a central role, extends directly to non-gauge theories with arbitrary
matter content (though non-linear sigma models are beyond the scope of the
current method).
