= Ordered-phase obstruction in a Gaussian scalar model
{title2=$m^2<0\Longrightarrow\inf_M(m^2M^2/2)=-\infty$}
The uniform mode of a pure <Gaussian field theory> with negative squared mass has an unbounded quadratic energy. Its <partition function> diverges even with a finite-volume ultraviolet regulator, so it supplies no stable ordered branch. At positive squared mass the zero-source average is zero. Thus the scaling dimension of the field can yield a formal <order-parameter critical exponent> without establishing a negative-reduced-temperature <magnetization> law. A stabilizing quartic interaction is relevant below four dimensions and ordinarily changes the critical theory to the <Wilson-Fisher fixed point>; above four its coefficient is a <dangerously irrelevant coupling> for the ordered phase.
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