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

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We study the phase transition and the critical behavior of the BTZ black hole with torsion obtained in $(1+2)$-dimensional Poincar\'{e} gauge theory.

• According to Ehrenfest's classification, when the parameters in the theory are arranged properly the BTZ black hole with torsion may posses the second order phase transition which is also a smaller mass/larger mass black hole phase transition.
• Nevertheless, the critical behavior is different from the one in the van der Waals liquid/gas system.
• We also calculated the critical exponents of the relevant thermodynamic quantities, which are the same as the ones obtained in the Ho\v{r}ava-Lifshitz black hole and the Born-Infeld black hole.