  The Berezinskii-Kosterlitz-Thouless (BKT) transitions of the six-state clock
model on the square lattice are investigated by means of the corner-transfer
matrix renormalization group method. A classical analog of the entanglement
entropy $S( L, T )$ is calculated for $L \times L$ square system up to $L =
129$, as a function of temperature $T$. The entropy exhibits a peak at $T =
T^*_{~}( L )$, where the temperature depends on both $L$ and the boundary
conditions. Applying the finite-size scaling to $T^*_{~}( L )$ and assuming
presence of the BKT transitions, the two distinct phase-transition temperatures
are estimated to be $T_1^{~} = 0.70$ and $T_2^{~} = 0.88$. The results are in
agreement with earlier studies. It should be noted that no thermodynamic
functions have been used in this study.
