  We present a necessary condition under which a collinear ferromagnet
Fe$_{1-x}A_{x}$ ($A={\rm Pt},{\rm Ni}$) with disordered face-centered-cubic
structure exhibits the Invar effect. The condition involves the rate at which
the fraction of Fe moments that are antiferromagnetically aligned with the
magnetization fluctuates as the system is heated, $dx^{{\rm Fe}\downarrow}/dT$.
Another contributing factor is the magnetostructural coupling
$\kappa=-(1/V)(\partial V / \partial x^{{\rm Fe}\downarrow})_{T}$, where the
volume $V(T, x^{{\rm Fe}\downarrow})$ corresponds to a homogeneous
ferromagnetic state, a partially disordered local moment state, or a disordered
local moment state depending on the value of $x^{{\rm Fe}\downarrow}$.
According to the criterion, the Invar phenomenon occurs only when the thermal
expansion arising from the temperature dependence of the fraction of Fe moments
which point down $-1/3\,\kappa\,dx^{{\rm Fe}\downarrow}/dT$ compensates for the
thermal expansion associated with the anharmonicity of lattice vibrations in a
wide temperature interval. Upon further investigation, we provide evidence that
only alloys with strong magnetostructural coupling at zero Kelvin can show the
Invar effect.
