Ruppeiner Geometry of (2 + 1)-Dimensional Spinning Dilaton Black Hole

In this paper, we study the geometrothermodynamics of(2 + 1)-dimensional spinning dilaton black hole. We show that the Ruppeiner curvature vanishes, which implies that there exist no phase transitions and thermodynamic interactions. However when the thermodynamics fluctuation is included, the geometry structure is reconsidered. The non-vanishing Ruppeiner curvature is obtained, which means the phase space is non-flat. We also study the phase transitions and show that it can indeed take place at some points. (general)