  We probe for statistical and Coulomb induced spin textures among the
low-lying states of repulsively-interacting particles confined to potentials
that are both rotationally and time-reversal invariant. In particular, we focus
on two-dimensional quantum dots and employ configuration-interaction techniques
to directly compute the correlated many-body eigenstates of the system. We
produce spatial maps of the single-particle charge and spin density and verify
the annular structure of the charge density and the rotational invariance of
the spin field. We further compute two-point spin correlations to determine the
correlated structure of a single component of the spin vector field. In
addition, we compute three-point spin correlation functions to uncover chiral
structures. We present evidence for both chiral and quasi-topological spin
textures within energetically degenerate subspaces in the three- and
four-particle system.
