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We study hysteresis in the random-field Ising model with an asymmetricdistribution of quenched fields, in the limit of low disorder in two and threedimensions. We relate the spin flip process to bootstrap percolation, and showthat 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 disorderstrength $\Delta$ much less than the exchange coupling J. For system size $1 <<L < L^*$, the coercive field $h_{coer}$ varies as $2J - \Delta \ln \ln L$ forthe 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 cubiclattices. For lattices with coordination number 3, the limiting magnetizationshows no jump, and $h_{coer}$ tends to J.Comment: 4 pages, 4 figure

Hysteresis in the Random-Field Ising Model and Bootstrap Percolation