Nonequilibrium Phase Transitions and a Nonequilibrium Critical Point from Anti-de Sitter Space and Conformal Field Theory Correspondence

We find novel phase transitions and critical phenomena that occur only outside the linear-response regime of current-driven nonequilibrium states. We consider the strongly-interacting (3+1)-dimensional N=4 large-Nc SU(Nc) supersymmetric Yang-Mills theory with a single flavor of fundamental N=2 hypermultiplet as a microscopic theory. We compute its nonlinear non-ballistic quark-charge conductivity by using the AdS/CFT correspondence. We find that the system exhibits a novel nonequilibrium first-order phase transition where the conductivity jumps and the sign of the differential conductivity flips at finite current density. A nonequilibrium critical point is discovered at the end point of the first-order regime. We propose a nonequilibrium steady-state analogue of thermodynamic potential in terms of the gravity-dual theory in order to define the transition point. Nonequilibrium analogues of critical exponents are proposed as well. The critical behavior of the conductivity is numerically confirmed on the basis of these proposals. The present work provides a new example of nonequilibrium phase transitions and nonequilibrium critical points.