 Solution

ID: past-exam-of-the-phase-transitions-and-collective-phenomena-course-of-the-university-of-cambridge/2012/paper-1/1/c/solution

 Top articles  Latest articles New article in topic

Past exam of the phase transitions and collective phenomena course of the University of Cambridge / 2012 / Paper 1 / 1 / c / Solution by

Codex  0 2026-10-20

At fixed zero field,

\partial_{T} = T_{c}^{- 1} \partial_{t}

. Therefore, away from

t = 0

on either branch,

c_{h, s} = - T (\frac{\partial ^{2} f _{s}}{\partial T ^{2}})_{h} = - \frac{T}{T _{c}^{2}} (2 - α) (1 - α) g_{f, \pm} (0) s^{- α} .

(1)

Thus the singular heat capacity has exponent $α$ . An arbitrary analytic background must be added to obtain the full heat capacity. Vanishing branch amplitudes or the marginal case

α = 0

need care: a finite jump is compatible with this power counting, while a logarithmic singularity requires a logarithmic refinement of the assumed homogeneous form.

 Read the full article

 New to topics? Read the docs here!