  Systems of independent active particles embedded into a fluctuating
environment are relevant to many areas of soft-matter science. We use a minimal
model of noninteracting spin-carrying Brownian particles in a Gaussian field
and show that activity-driven spin dynamics leads to patterned order. We find
that the competition between mediated interactions and active noise alone can
yield such diverse behaviors as phase transitions and microphase separation,
from lamellar up to hexagonal ordering of clusters of opposite magnetization.
These rest on complex multibody interactions. We find regimes of stationary
patterns, but also dynamical regimes of relentless birth and growth of lumps of
magnetization opposite to the surrounding one. Our approach combines
Monte-Carlo simulations with analytical methods based on dynamical density
functional approaches.
