 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-3/35e/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Mean field replaces edge and triangle products by

m^{2}

and

m^{3}

. There are

3 N

edges and

2 N

elementary triangles, so

Z_{N} ≃ M \sum (( N + M ) /2 N) exp {βN (B m + 3 J m^{2} + 2 K m^{3})} .

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