Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-303/3/a/v/solution

For , the quartic coupling has , but setting it to zero removes the stabilizing term. It is a dangerously irrelevant coupling. At , minimizing gives and . This is consistent with Gaussian scaling because
For , flows to a nonzero Wilson-Fisher fixed point, so no dangerously irrelevant zero-coupling limit spoils the ordinary scaling relations.
Solved by gpt-5.6-sol high.

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