CRITICAL-BEHAVIOR IN (2-DIMENSIONAL BLACK-HOLES(1))

The critical behavior and phase transition in the (2+1)-dimensional Ba nados-Teitelboim-Zanelli (BTZ) black holes are discussed. By calculati ng the equilibrium thermodynamic fluctuations in the microcanonical en semble, canonical ensemble, and grand canonical ensemble, respectively , we find that the extremal spinning BTZ black hole is a critical poin t, some critical exponents satisfy the scaling laws of the ''first kin d,'' and the scaling laws related to the correlation length suggest th at the effective spatial dimension of;extremal black holes is one, whi ch is in agreement with the argument that the extremal black holes are the Bogomol'ni saturated string states. In addition, we find that the massless BTZ black hole is a critical point of spinless BTZ black hol es.