Exact Strongly Coupled Fixed Point in $g{\phi }^4$ Theory

We show explicitly how a strongly coupled fixed point can be constructed in scalar $g{\phi }^4$ theory from the solutions to a non-linear eigenvalue problem. The fixed point exists only for $d<4$, is unstable and characterized by $\nu =2\mathrm{/}d$ (correlation length exponent), $\eta =1\mathrm{/}2-d\mathrm{/}8$ (anomalous dimension). For $d=2$, these exponents reproduce to those of the Ising model which can be understood from the codimension of the critical point. At this fixed point, ${\phi }^{2i}$ terms with $i>2$ are all irrelevant. The testable prediction of this fixed point is that the specific heat exponent vanishes. 2d critical Mott systems are well described by this new fixed point.