Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-344/2/a/solution

For a uniform field the gradient term vanishes and minimization over gives
When , the nonzero minimum has
while its direction is arbitrary by rotational symmetry. A sudden quench creates many independently oriented domains. Their mismatches contain gradients and topological defects, whose motion and pair annihilation are slow, so the uniform state is not reached promptly.

New to topics? Read the docs here!