Disorder, order, and domain wall roughening in the two-dimensional random field Ising model

Ground states and domain walls are investigated with exact combinatorial optimization in two-dimensional random field Ising magnets. The ground states break into domains above a length scale that depends exponentially on the random field strength squared. For weak disorder, this paramagnetic structure has remnant longrange order of the percolation type. The domain walls are super-rough in ordered systems with a roughness exponent z close to 6/5. The interfaces exhibit rare fluctuations and multiscaling reminiscent of some models of kinetic roughening and hydrodynamic turbulence. @S1063-651X~98!51511-5#