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

TL;DR

This paper explores the behavior of ground states and domain walls in the 2D random field Ising model, revealing how disorder influences domain formation, roughening, and interface fluctuations.

Contribution

It provides exact combinatorial optimization analysis of ground states and domain walls, highlighting the effects of disorder strength on domain structure and interface roughness.

Findings

Domains form above a size scale depending exponentially on disorder strength

Domain walls are super-rough with a roughness exponent near 6/5

Interfaces show rare fluctuations and multiscaling similar to kinetic roughening

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 $\zeta$ close to 6/5. The interfaces exhibit rare fluctuations and multiscaling reminiscent of some models of kinetic roughening and hydrodynamic turbulence.