Solution

ID: past-exam-of-the-condensed-matter-physics-course-of-the-university-of-oxford/2018/4/d/solution

Ferromagnetic interactions enhance the response above the ordering transition. The Curie–Weiss law improves the independent-spin approximation:
with positive Weiss temperature and the same high-temperature coefficient . In a simple mean-field theory, take . More generally is fitted and need not equal , and the simple pole does not give exact critical behaviour arbitrarily close to the transition.
At zero temperature, a selected ferromagnetic orientation has all magnetic moments aligned. Its saturation magnetization is
Equivalently, there are per conventional cell. The moment points along either allowed easy-axis direction at zero magnetic field. This is the local or single-domain spontaneous magnetization; a macroscopic multidomain sample can have smaller, even zero, net magnetization in the absence of a selecting field.

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