Re-entrant phase transitions in non-commutative quantum mechanics

We discuss the (2+1)-dimensional Dirac oscillator in a magnetic field in non commutative quantum mechanics. The system is known to be characterised by a left right- chiral phase transition in ordinary Quantum mechanics. We show that the momentum noncommutativity shifts the know phase transition while the space non commutativity introduces a new right-left chiral quantum phase transition giving rise to the intriguing phenomenon of re-entrant phase transition observed in condensed matter as well as in black hole physics. (paper)