Analytical investigation of the specific heat for the Cantor energy spectrum

• The exact analytical expression for the specific heat at all temperatures is obtained.
• The exact expression for the limit dividing the oscillating/non-oscillating regimes is obtained.

For the energy spectrum obtained for monoscale Cantor set the correct analytical calculations of the specific heat in the frame of the Boltzmann–Maxwell statistics have been performed. These evaluations were realized with the help of Mellin's transform. The accurate analytical expressions for the specific heat in all temperature range were obtained. They demonstrate the log-periodic behavior in low-temperature and non-oscillatory behavior in high-temperature regions, accordingly. The accurate value of the limiting temperature determining the boundary between these two regions was found and evaluated.