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

We study the phase transition and the critical behavior of the BTZ black hole with torsion obtained in $(1+2)$-dimensional Poincaré 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 Hořava-Lifshitz black hole and the Born-Infeld black hole.