Abstract
We extended the three dimensional ideal Bose gas theory into the fractal dimensions between 2 and 3. The thermodynamic properties and critical exponents of the ideal Bose gas are studied through the functional analysis of the Bose gas function in the fractal dimensions. The condensation and phase transition of the ideal system depend on its dimensions. The phase transition is detectable only in the sufficiently high derivatives of the specific heat function. The derivatives change discontinuously at values of the fractal dimensions which we have calculated.
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