Disorder, Order, and Domain Wall Roughening in the 2d Random Field Ising Model

Physics – Condensed Matter – Disordered Systems and Neural Networks

Scientific paper

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to be published in Phys.Rev.E/Rapid.Comm

Scientific paper

10.1103/PhysRevE.58.R5217

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 long-range order of the percolation type. The domain walls are super-rough in ordered systems with a roughness exponent $\zeta$ close to 6/5. The interfaces exhibit rare fluctuations and multiscaling reminiscent of some models of kinetic roughening and hydrodynamic turbulence.

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