PV criticality of Achucarro-Ortiz black hole in the presence of higher-order quantum and GUP corrections

In this paper, we study the quantum-corrected and generalizedf uncertinty principle (GUP)-corrected thermodynamics of the (2 + 1)-dimensional charged-rotating Achucarro-Ortiz (AO) black hole. The corrected parameters include temperature, entropy, and heat capacity which help to investigate the instability phases of the Achucarro-Ortiz black hole. We show that this black hole with small mass possesses unstable regions. However, we reveal that those instabilities can be removed by the GUP corrections. Finally, we also compute the maximum temperature that can be reached by the Achucarro-Ortiz black hole. We show that corrected temperatures by different methods we used are identical at the small mass limit, hence GUP correction at small mass limit is a quantum gravity correction. Interestingly, we show by graphical analysis that leading-order quantum-corrected temperature of the Achucarro-Ortiz black hole behaves similar to the GUP-corrected temperature of uncharged Achucarro-Ortiz black hole.