Yang-Yang anomaly

The Yang-Yang anomaly provides (Eq. 3):

\[C_V = VT \left. \frac{\partial^2 p}{\partial T^2} \right\vert_V -NT \left. \frac{\partial^2 \mu}{\partial T^2} \right\vert_V \]

where \(C_V\) is the heat capacity at constant volume and \(\mu\) is the chemical potential. Given that experimentally it is found that \(C_V\) diverges at the critical temperature this implies that either \(\partial^2 p/\partial T^2\) or \(\partial^2 \mu/\partial T^2\), or both, diverge as \(T \rightarrow T_c^-\). Fisher and Orkoulas showed that both terms diverge.