Lattice approximation to the dynamical Φ₃⁴ model

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We study the lattice approximations to the dynamical Φ⁴₃ model by paracontrolled distributions proposed in [GIP13]. We prove that the solutions to the lattice systems converge to the solution to the dynamical Φ₃⁴ model in probability, locally in time. The dynamical Φ₃⁴ 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.