Abstract
Pair exchange parameters ${J}_{ij}$ of the classical Heisenberg Hamiltonian for magnetic interactions in the archetypical Invar system, face centered cubic (fcc) $\mathrm{Fe}\ensuremath{-}\mathrm{Ni}$ alloys, are calculated from the first principles. The magnetic structure of $\mathrm{Fe}\ensuremath{-}\mathrm{Ni}$ alloys in the region of volumes and electron concentrations related to the Invar effect is highly frustrated. However, the origin of such a frustration in concentrated alloys and in the pure fcc Fe are different. While in Fe it is due to the long-range oscillating ${J}_{ij}$, in alloys with high Ni concentration it is mainly the consequence of a huge dispersion of the nearest-neighbor exchange parameters, caused by the local environment effects.
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