A one-dimensional kinetic Ising model with domain wall dynamics corresponding to diffusion-limited annihilation in the presence of particle sources is considered. The spin-spin correlation function C, is calculated exactly for a nonequilibrium steady state which can be brought close to a critical point of the system. We find that in contrast to equilibrium situations, C, contains two distinctly diverging correlation lengths ~ ~ ~ 42, where ~2 is a length closely related to the nonequilibrium kinetics of the system.
We report first-order mean-field results for nonequilibrium random-exchange lattice systems, namely, Ising-like models whose kinetics involve a simultaneous, random competition between ferromagnetic and antiferromagnetic interactions that generally induces nonequilibrium steady states. We consider the competition between symmetric bonds. \ifmmode\pm\else\textpm\fi{}
J0, symmetric bonds competing with broken ones, \ifmmode\pm\else\textpm\fi{}
J0 and J=0, nonsymmetric bonds, \ensuremath{\Vert}
J1\ensuremath{\Vert} and -\ensuremath{\Vert}
J2\ensuremath{\Vert}, and some of those systems under an external magnetic field h. The time evolution and steady-state properties, including phase diagrams, are obtained for several lattice coordination numbers, e.g., the case of simple-cubic lattices of dimension d\ensuremath{\le}3. A comparison is made with existing exact results for d=1, h=0, and \ifmmode\pm\else\textpm\fi{}
J0.
The dissipative transverse-field Ising (TFI) model provides a paradigmatic setting for nonequilibrium quantum many-body physics. We show that a class of boundary-driven TFI models subject to dissipation at only one boundary possesses hidden time-reversal symmetry, which enables an exact construction of their nonequilibrium steady states. The solution admits a matrix-product representation and defines a nonequilibrium partition function from which steady-state observables can be evaluated efficiently. We use the exact solution to characterize the microscopic structure of the steady state through its z-magnetization and two-point correlations. A striking feature is that the local field at the dissipative boundary governs the spatial organization of the steady state throughout the chain. The steady state typically exhibits boundary-localized magnetization profiles and exponentially decaying correlations, whose characteristic length scales are set by the dissipative boundary. In the weak-driving limit, suitably tuned boundary fields can reorganize the NESS into a delocalized single-interface structure, giving rise to long-range correlations that decay linearly with distance.