## Abstract

The structure of the three-dimensional (3D) random field Ising magnet is studied by ground-state calculations. We investigate the percolation of the minority-spin orientation in the paramagnetic phase above the bulk phase transition, located at [Δ/J]_{c} ≃ 2.27, where Δ is the standard deviation of the Gaussian random fields (J = 1). With an external field H there is a disorder-strength-dependent critical field ± H_{c}(Δ) for the down (or up) spin spanning. The percolation transition is in the standard percolation universality class. H_{c} ∼ (Δ - Δ_{p})δ, where Δ_{p} = 2.43 ± 0.01 and δ = 1.31 ± 0.03, implying a critical line for Δ_{c} < Δ ≤ Δ_{p}. When, with zero external field, Δ is decreased from a large value there is a transition from the simultaneous up- and down-spin spanning, with probability π_{↑↓} = 1.00 to π_{↑↓} = 0. This is located at Δ = 2.32 ± 0.01, i.e., above Δ_{c}. The spanning cluster has the fractal dimension of standard percolation, D_{f} = 2.53 at H = H_{c}(Δ). We provide evidence that this is asymptotically true even at H = 0 for Δ_{c} < Δ ≤ Δ_{p} beyond a crossover scale that diverges as Δ_{c} is approached from above. Percolation implies extra finite-size effects in the ground states of the 3D random field Ising model.

Original language | English |
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Article number | 144403 |

Pages (from-to) | 1-8 |

Number of pages | 8 |

Journal | Physical Review B |

Volume | 66 |

Issue number | 14 |

DOIs | |

Publication status | Published - 1 Oct 2002 |

MoE publication type | A1 Journal article-refereed |