# Why the heat capacity doesn't diverge in the Kosterlitz-Thouless (KT) phase transition?

The KT transition has a special properties that, during the phase transition the heat capacity stay finite (so the behaviour of the heat capacity cannot reflect any critical behaviours). However, the correlation length and the susceptibility diverge. Specifically, $\xi \sim exp(b |t|^{-\nu})$ and $\chi \sim \xi^{2-\eta}$, where $t$ is the reduced temperature, $b$ is some constant, and $\nu$ and $\eta$ are critical exponents.

I understand that, in this case the correlation diverges so fast comparing to the first/second order phase transition, but how this leads to the non-divergence behaviour of the heat capacity?