 Solution

ID: past-exam-of-the-theoretical-physics-i-course-of-the-university-of-cambridge/2013/paper-1/6/b/solution

Equilibrium requires

h = am + b m^{3}

. On the critical isotherm

a = 0

, so

h = b m^{3}, m = sgn (h) ∣ h / b ∣^{1/3}, δ = 3.

Here

δ

is defined by

h \propto sgn (m) ∣ m ∣^{δ}

at the critical temperature, or equivalently

∣ m ∣ \propto ∣ h ∣^{1/ δ}

. The positive quartic coefficient selects a stable equilibrium, including the flat but stable zero-field thermodynamic critical point.

 New to topics? Read the docs here!