= Solution
The inverse-susceptibility curve has a Curie–Weiss form above $T_C$ and vanishes on approach to it. The material can have <spontaneous magnetization> for $T<T_C$, including the zero-temperature limit, whereas for $T>T_C$ its zero-field equilibrium state is paramagnetic. At a continuous transition the spontaneous moment tends to zero at $T_C$; divergence of differential susceptibility there is not a finite saturated permanent moment.
A simple <Weiss molecular field> model takes the effective internal field intensity to be $H_{\rm eff}=H+\Lambda M$, with positive coupling $\Lambda$. Let $C$ be the independent-moment Curie constant. Linearizing the single-ion response on the high-temperature side gives
$$
M=\frac CT(H+\Lambda M),\qquad
\boxed{\chi_M=\frac C{T-T_C},\quad T_C=\Lambda C,\quad
\frac1{\chi_M}=\frac{T-T_C}{C}.}
$$
This explains the straight upper branch and its positive <temperature> intercept. At $T_C$ the zero-field linearized response diverges; finite field, finite size and critical fluctuations limit its use. For a spin-only two-state mean-field model the full equation is $m=\tanh[(T_C/T)m+\mu_B\mu_0H/(k_BT)]$, with $m=M/(N\mu_B)$; below $T_C$ it has nonzero zero-field solutions.
An ordering scale near $1000\,\mathrm K$ corresponds to $k_BT_C\simeq0.086\,\mathrm{eV}$, about four orders of magnitude larger than the preceding dipolar pair scale. <Exchange interaction> can supply such energies: the Pauli antisymmetry of overlapping <electron> states changes their spatial correlations and hence Coulomb and kinetic energies according to their <spin> configuration. An effective ferromagnetic coupling can favor parallel moments. It is not simply the classical <magnetic field> of a neighbouring dipole. For example, with the convention $\mathcal H=-J\sum_{\langle ij\rangle}\mathbf S_i\cdot\mathbf S_j$ and $J>0$, the localized-spin mean-field scale is $k_BT_C=zJS(S+1)/3$; this illustrates why an atomic electronic interaction, rather than a bare dipolar field, can produce a high transition <temperature>.
\Image[/past-exam-of-the-condensed-matter-physics-course-of-the-university-of-oxford/2014-independent-spins-and-weiss-ordering.png]
{title=Independent-spin saturation and spontaneous order in a specified mean-field model}
{description=Original calculated curves. The left panel compares $\tanh x$ to its weak-field linearization. The right panel solves the zero-field spin-one-half mean-field equation $m=\tanh(m/t)$ on the positive spontaneous branch, with $t=T/T_C$. It depicts one <magnetic domain>; cancellation between domains is a separate macroscopic effect.}
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