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

We consider the Langevin lattice dynamics for a spontaneously broken λ ϕ 4 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.