  We investigate the effect of chemical disorder on the magnetic exchange
couplings and the Curie temperature ($T_{\text{c}}$) in L1$_0$-ordered FeNi
using first-principles-based calculations. We use supercells to model chemical
disorder, to account for the specific symmetry-broken local chemical
environments around the individual atoms. We find a very strong variation of
the most dominant first-nearest neighbor Fe-Fe interaction for different
inequivalent Fe-Fe pairs, ranging from around 5 meV to 37 meV, compared to a
coupling strength of 27 meV in the ordered state. To estimate the influence of
such strong variations of the magnetic coupling constants on the Curie
temperature of the disordered or partially ordered state, we study a simple
Heisenberg model with random Gaussian-distributed nearest neighbor couplings on
an fcc lattice. Our Monte Carlo simulations for this model indicate that
strongly varying exchange couplings, such as those obtained for FeNi, can lead
to a reduction of $T_{\text{c}}$ of around 10% relative to the one obtained
using only the average coupling.
