  Low energy effective theories give access to regimes of the QCD phase diagram
that to date are hard to simulate directly with lattice QCD or with functional
approaches. For lattice QCD this includes the small temperature and/or large
density regime. In both regimes the lower UV cutoff in low energy effective
theories may soften computational problems. Moreover, lattice results for low
energy effective theories serve as benchmark results for functional approaches
for these effective theories. Here we present lattice results for the scalar
O($4$) and quark-meson models. We simulate the theory via Stochastic
Quantisation and report on the effects of employing coloured noise, a method
that allows control over the momentum scale of the simulation.
