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Percolation in three-dimensional random field Ising magnets
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© 2002 American Physical Society (APS). This is the accepted version of the following article: Seppälä, E. T. & Pulkkinen, A. M. & Alava, Mikko J. 2002. Percolation in three-dimensional random field Ising magnets. Physical Review B. Volume 66, Issue 14. 144403/1-8. ISSN 1550-235X (electronic). DOI: 10.1103/physrevb.66.144403, which has been published in final form at http://journals.aps.org/prb/abstract/10.1103/PhysRevB.66.144403.
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School of Science |
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Seppälä, E. T.
Pulkkinen, A. M.
Alava, Mikko J.
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en
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144403/1-8
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Physical Review B, Volume 66, Issue 14
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 ±Hc(Δ) for the down (or up) spin spanning. The percolation transition is in the standard percolation universality class. Hc∼(Δ−Δp)δ, where Δp=2.43±0.01 and δ=1.31±0.03, implying a critical line for Δc<Δ<~Δp. 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 Δc. The spanning cluster has the fractal dimension of standard percolation, Df=2.53 at H=Hc(Δ). We provide evidence that this is asymptotically true even at H=0 for Δc<Δ<~Δp beyond a crossover scale that diverges as Δc is approached from above. Percolation implies extra finite-size effects in the ground states of the 3D random field Ising model.
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Seppälä, E. T. & Pulkkinen, A. M. & Alava, Mikko J. 2002. Percolation in three-dimensional random field Ising magnets. Physical Review B. Volume 66, Issue 14. 144403/1-8. ISSN 1550-235X (electronic). DOI: 10.1103/physrevb.66.144403.