Susceptibility and percolation in two-dimensional random field Ising magnets

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.author Seppälä, E. T.
dc.contributor.author Alava, Mikko J.
dc.date.accessioned 2015-12-02T10:02:18Z
dc.date.available 2015-12-02T10:02:18Z
dc.date.issued 2001
dc.identifier.citation Seppälä, E. T. & Alava, Mikko J. 2001. Susceptibility and percolation in two-dimensional random field Ising magnets. Physical Review E. Volume 63, Issue 6. 066109/1-14. ISSN 1539-3755 (printed). DOI: 10.1103/physreve.63.066109. en
dc.identifier.issn 1539-3755 (printed)
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/18930
dc.description.abstract The ground-state structure of the two-dimensional random field Ising magnet is studied using exact numerical calculations. First we show that the ferromagnetism, which exists for small system sizes, vanishes with a large excitation at a random field strength-dependent length scale. This breakup length scale Lb scales exponentially with the squared random field, exp(A/Δ2). By adding an external field H, we then study the susceptibility in the ground state. If L>Lb, domains melt continuously and the magnetization has a smooth behavior, independent of system size, and the susceptibility decays as L−2. We define a random field strength-dependent critical external field value ±Hc(Δ) for the up and down spins to form a percolation type of spanning cluster. The percolation transition is in the standard short-range correlated percolation universality class. The mass of the spanning cluster increases with decreasing Δ and the critical external field approaches zero for vanishing random field strength, implying the critical field scaling (for Gaussian disorder) Hc∼(Δ−Δc)δ, where Δc=1.65±0.05 and δ=2.05±0.10. Below Δc the systems should percolate even when H=0. This implies that even for H=0 above Lb the domains can be fractal at low random fields, such that the largest domain spans the system at low random field strength values and its mass has the fractal dimension of standard percolation Df=91/48. The structure of the spanning clusters is studied by defining red clusters, in analogy to the “red sites” of ordinary site percolation. The sizes of red clusters define an extra length scale, independent of L. en
dc.format.extent 066109/1-14
dc.format.mimetype application/pdf en
dc.language.iso en en
dc.publisher American Physical Society (APS) en
dc.relation.ispartofseries Physical Review E en
dc.relation.ispartofseries Volume 63, Issue 6
dc.rights © 2001 American Physical Society (APS). This is the accepted version of the following article: Seppälä, E. T. & Alava, Mikko J. 2001. Susceptibility and percolation in two-dimensional random field Ising magnets. Physical Review E. Volume 63, Issue 6. 066109/1-14. ISSN 1539-3755 (printed). DOI: 10.1103/physreve.63.066109, which has been published in final form at http://journals.aps.org/pre/abstract/10.1103/PhysRevE.63.066109. en
dc.subject.other Physics en
dc.title Susceptibility and percolation in two-dimensional random field Ising magnets en
dc.type A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä fi
dc.description.version Peer reviewed en
dc.rights.holder American Physical Society (APS)
dc.contributor.school Perustieteiden korkeakoulu fi
dc.contributor.school School of Science en
dc.contributor.department Teknillisen fysiikan laitos fi
dc.contributor.department Department of Applied Physics en
dc.subject.keyword Ising model en
dc.subject.keyword domain walls en
dc.subject.keyword domain structures en
dc.subject.keyword random magnets en
dc.subject.keyword percolation studies of phase transitions en
dc.identifier.urn URN:NBN:fi:aalto-201512015460
dc.type.dcmitype text en
dc.identifier.doi 10.1103/physreve.63.066109
dc.type.version Final published version en


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