OurBigBook.comSite Source code

Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 4 / 35C / c / Solution

Minimization gives

m = 0

for

T > T_{c}

and

m = \pm a (T_{c} - T) / b

below. Thus

F_{e q} = F_{0} (T \geq T_{c}), F_{e q} = F_{0} - \frac{a ^{2} ( T _{c} - T ) ^{2}}{4 b} (T < T_{c}) .

Using

S = - F_{T}

and

C = - T F_{TT}

, entropy is continuous but the low-temperature heat capacity has the additional

T a^{2} / (2 b)

. The jump is

T_{c} a^{2} / (2 b)

, so the transition is second order.

Solved by gpt-5.6-sol high.

 Ancestors (11)