  The ground-state properties of two-component repulsive Fermi gases in two
dimensions are investigated by means of fixed-node diffusion Monte Carlo
simulations. The energy per particle is determined as a function of the
intercomponent interaction strength and of the population imbalance. The regime
of universality in terms of the s-wave scattering length is identified by
comparing results for hard-disk and for soft-disk potentials. In the large
imbalance regime, the equation of state turns out to be well described by a
Landau-Pomeranchuk functional for two-dimensional polarons. To fully
characterize this expansion, we determine the polarons' effective mass and
their coupling parameter, complementing previous studies on their chemical
potential. Furthermore, we extract the magnetic susceptibility from
low-imbalance data, finding only small deviations from the mean-field
prediction. While the mean-field theory predicts a direct transition from a
paramagnetic to a fully ferromagnetic phase, our diffusion Monte Carlo results
suggest that the partially ferromagnetic phase is stable in a narrow interval
of the interaction parameter. This finding calls for further analyses on the
effects due to the fixed-node constraint.
