Hysteresis in the Random Field Ising Model and Bootstrap Percolation

Details Hysteresis in the Random Field Ising Model and Bootstrap Percolation Hysteresis in the Random Field Ising Model and Bootstrap Percolation

2002-04-29

arxiv.org/abs/cond-mat/0204618v1

Phys. Rev. Lett. 88, 197202 (2002)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.88.197202

We study hysteresis in the random-field Ising model with an asymmetric distribution of quenched fields, in the limit of low disorder in two and three dimensions. We relate the spin flip process to bootstrap percolation, and show that the characteristic length for self-averaging $L^*$ increases as $exp(exp (J/\Delta))$ in 2d, and as $exp(exp(exp(J/\Delta)))$ in 3d, for disorder strength $\Delta$ much less than the exchange coupling J. For system size $1 << L < L^*$, the coercive field $h_{coer}$ varies as $2J - \Delta \ln \ln L$ for the square lattice, and as $2J - \Delta \ln \ln \ln L$ on the cubic lattice. Its limiting value is 0 for L tending to infinity, both for square and cubic lattices. For lattices with coordination number 3, the limiting magnetization shows no jump, and $h_{coer}$ tends to J.

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