Lattice approximation to the dynamical ${\mathrm{\Phi }}_3^4$ model

We study the lattice approximations to the dynamical ${\mathrm{\Phi }}_3^4$ model by paracontrolled distributions proposed in [GIP13]. We prove that the solutions to the lattice systems converge to the solution to the dynamical ${\mathrm{\Phi }}_3^4$ model in probability, locally in time. The dynamical ${\mathrm{\Phi }}_3^4$ model is not well defined in the classical sense. Renormalisation has to be performed in order to define the non-linear term. Formally, this renormalisation corresponds to adding an infinite mass term to the equation which leads to adding a drift term in the lattice systems.