Critical behaviors of a (2 + 1)-dimensional black hole with a nonlinear electrodynamics source

On the basis of a charged BTZ black hole, we add an extra term in the metric function to describe the contribution from nonlinear electrodynamics. In this way we artificially construct a (2 + 1)-dimensional black hole in general relativity coupled with a nonlinear electrodynamics source. The thermodynamic quantities and Smarr formula are derived. It is found that this black hole has T - S criticality like that of an RN-AdS black hole. Further modifying the metric function, we obtain a (2 + 1)-dimensional black hole possessing P - V critical behaviors similar to that of van der Waals fluid. To our knowledge, this is the first example of (2 + 1)-dimensional black holes having this kind of critical behavior.