Continuous phase transition and critical behaviors of 3D black hole with torsion

Abstract

We study the phase transition and the critical behavior of the BTZ black hole\nwith torsion obtained in $(1+2)$-dimensional Poincar\\'{e} gauge theory.\nAccording to Ehrenfest's classification, when the parameters in the theory are\narranged properly the BTZ black hole with torsion may posses the second order\nphase transition which is also a smaller mass/larger mass black hole phase\ntransition. Nevertheless, the critical behavior is different from the one in\nthe van der Waals liquid/gas system. We also calculated the critical exponents\nof the relevant thermodynamic quantities, which are the same as the ones\nobtained in the Ho\\v{r}ava-Lifshitz black hole and the Born-Infeld black hole.\n