Microstructure and Continuous Phase Transition of the Gauss-Bonnet AdS Black Hole

The phase transition of the Gauss-Bonnet AdS black hole has the similar property with the van der Waals thermodynamic system. However, it is determined by the Gauss-Bonnet coefficient {\alpha}, not only the horizon radius. Furthermore, the phase transition is not the pure one between a big black hole and a small black hole. With this issue, we introduce a new order parameter to investigate the critical phenomenonand to give the microstructure explanation of the Gauss-Bonnet AdS black hole phase transition. And the critical exponents are also obtained. At the critical pointof the Gauss-Bonnet AdS black hole, we reveal the microstructure of the black hole by investigating the thermodynamic geometry. These results perhaps provide some certain help to deeply explore the black hole microscopic structure and to build the quantum gravity.Comment: 19 pages, 11figure