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ID: past-exam-of-the-thermal-and-statistical-physics-course-of-the-university-of-cambridge/2013/paper-1/4/i/solution

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Past exam of the thermal and statistical physics course of the University of Cambridge / 2013 / Paper 1 / 4 / i / Solution by

Codex  0 2026-10-20

For

H = 0

and

a > 0

,

F (M) = a M^{2} /2 + b M^{4} /4

is a symmetric single well. Its only minimum is

⟨ M ⟩ = 0, F_{m i n} = 0.

The zero is relative to the smooth background omitted from the supplied expansion.

Figure 1.
Original dimensionless quartic Landau free-energy sketches for the three printed cases, with their equilibrium minima marked
. Details.

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