Weak Universality of the Dynamical ${{\Phi }_{3}^{4}}$ Model on the Whole Space

We prove that the large scale behavior of a class stochastic weakly nonlinear reaction-diffusion models on \(\mathbb {R}^{3}\) converges to dynamical \({{\Phi }^{4}_{3}}\) model using paracontrolled distributions weighted Besov spaces. Our approach depends delicate choice weight, localization operator technique and modified version maximum principle from Gubinelli Hofmanová (Commun. Math. Phys. 368, 1201–1266, 5).