Past exam of the physics course of the year 4 of the natural sciences course of the University of Cambridge / 2016 / Paper 1 / Section B / B1 / c / Solution

For $g>0$, $B\to +\infty$ at fixed $T>0$ selects $m=-J$, so all moments align with the field:This is magnetic saturation. The Curie response of an arbitrary independent spin follows at weak field: $\coth z=z^{-1}+z/3+O(z^3)$ givesThis is the Curie law of independent moments with paramagnetism. Thermal populations are symmetric at zero field, so the model has no spontaneous magnetization. Both limits hold at fixed positive temperature; taking $T\to 0$ first is a different limiting procedure.