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

E. T. Seppala·V. Petaja·M. J. Alava
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Abstract

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 $ζ$ 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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E. T. Seppala, V. Petaja, M. J. Alava. 1998-10-28. Disorder, Order, and Domain Wall Roughening in the 2d Random Field Ising Model. https://doi.org/10.1103/physreve.58.r5217

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