Thermodynamics of a Static Dilaton Black Hole

The thermodynamics of a static dilaton black hole is investigated by Euclidean path integral.Four interesting results are obtained:(Ⅰ)Although the temperature,heat capacity and chemical potential have different forms as compared to general classical static charged black hole,the Bardeen-Carter-Hawking thermodynamical laws are valid for the black hole.(Ⅱ)The entropy and area of the event horizon are zero but the energy,temperature and surface gravity are non-zero for extremal case(rh=2M=b).(Ⅲ)The charged black hole does not possess second order phase transitions as the Reissner-Nordstrom black hole since its heat capacity is negative.(Ⅳ)The action is equal to the entropy,and both quantities coincide with one quarter of area of the event horizon.