Thermodynamics of AdS-Schwarzschild-like black hole in loop quantum gravity

Under the assumption that loop quantum gravity (LQG) won't couple with the cosmological constant, we obtained the metric of Schwarzschild-like black hole with LQG correction in anti-de Sitter (AdS) space-time, and investigated its thermodynamics, including equation of state, criticality and Joule-Thomson expansion. We drew P-v graph and calculated the critical point. It is found that properties near the critical point is similar to Van der Waals system, with exactly the same critical exponents, and a critical ration $7/18$, which is slightly bigger than Van der Waals model $3/8$. Joule-Thomson expansion is also studied. It is interesting that compared with Schwarzschild-AdS black hole, LQG effect will bring inversion points. The inversion curve will divide T-P coordinate system into two zones: heating region and cooling region, which is shown in inversion curves and isenthalpic curves detailedly. And the minimum inversion mass is obtained.