  Classical 2D clock model is known to have a critical phase with
Berezinskii-Kosterlitz-Thouless(BKT) transitions. These transitions have
logarithmic corrections which make numerical analysis difficult. In order to
resolve this difficulty, one of the authors has proposed the method called
level spectroscopy, which is based on the conformal field theory. We extend
this method to the multi-degenerated case. As an example, we study the
classical 2D 6-clock model which can be mapped to the quantum self-dual 1D
6-clock model. Additionally, we confirm that the self-dual point has a precise
numerical agreement with the analytical result, and we argue the degeneracy of
the excitation states at the self-dual point from the effective field
theoretical point of view.
