 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2015/ii/paper-4/32c/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-06

Z = \sum_{{s}} e^{- βE}

\partial_{B} lo g Z = β ⟨ \sum_{i} s_{i} ⟩

. Thus the average spin per particle, or magnetization in these units, is

m = (Nβ)^{- 1} \partial_{B} lo g Z

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