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

At fixed zero field, ${\partial }_T=T_c^{-1}{\partial }_t$. Therefore, away from $t=0$ on either branch,Thus the singular heat capacity has exponent $\alpha$. An arbitrary analytic background must be added to obtain the full heat capacity. Vanishing branch amplitudes or the marginal case $\alpha =0$ need care: a finite jump is compatible with this power counting, while a logarithmic singularity requires a logarithmic refinement of the assumed homogeneous form.