Langevin simulation of scalar fields: Additive and multiplicative noises and lattice renormalization

We consider the Langevin lattice dynamics for a spontaneously broken λϕ4 scalar field theory where both additive and multiplicative noise terms are incorporated. The lattice renormalization for the corresponding stochastic Ginzburg–Landau–Langevin and the subtleties related to the multiplicative noise are investigated. ► We examine lattice Langevin equations in three spatial dimensions. ► Lattice dependence, regularization and renormalization for the Langevin system were studied. ► Additive and multiplicative noise cases where shown to be consistent with the lattice counterterms computed.