Renormalization destroys a finite time bifurcation in the ${\mathrm{\Phi }}_2^4$ equation

We study the singular ${\mathrm{\Phi }}_2^4$ equation at a pitchfork bifurcation of the underlying deterministic dynamics. To this aim, we linearize the SPDE along its stationary solution and show that the support of its finite-time Lyapunov exponents (FTLEs) is the real line, regardless of the bifurcation parameter and in sharp contrast to the non-singular ${\mathrm{\Phi }}_1^4$ equation. The proof relies on a support theorem for the stationary solution and its renormalized square.