Disorder, order, and domain wall roughening in the two-dimensional random field Ising model

Seppälä, Eira T.; Petäjä, Viljo; Alava, Mikko J.

doi:10.1103/physreve.58.r5217

Cited by 47 publications

(50 citation statements)

References 31 publications

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“…These arguments led to a critical dimension d c = 2. Numerical evidence [19,20] shows roughening of domain walls and the ground state breaking into domains above a length scale that depends exponentially on the random field strength squared, further strengthened the argument that d c = 2. Experiments on 2d dilute antiferromagnets, showed that no long-range ordering is present [21,22], but a possibility of first order transition in 3d has been observed [23].…”

Section: Introductionmentioning

confidence: 83%

Effect of increasing disorder on domains of the 2d Coulomb glass

Bhandari¹,

Malik²

2017

J. Phys.: Condens. Matter

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Abstract. We have studied a two dimensional lattice model of Coulomb glass for a wide range of disorders at T ∼ 0. The system was first annealed using Monte Carlo simulation. Further minimization of the total energy of the system was done using Baranovskii et al algorithm followed by cluster flipping to obtain the pseudo ground states. We have shown that the energy required to create a domain of linear size L in d dimensions is proportional to L d−1 . Using Imry-Ma arguments given for random field Ising model, one gets critical dimension d c ≥ 2 for Coulomb glass. The investigations of domains in the transition region shows a discontinuity in staggered magnetization which is an indication of a first-order type transition from charge-ordered phase to disordered phase. The structure and nature of Random field fluctuations of the second largest domain in Coulomb glass are inconsistent with the assumptions of Imry and Ma as was also reported for random field Ising model. The study of domains showed that in the transition region there were mostly two large domains and as disorder was increased, the two large domains remained but there were a large number of small domains. We have also studied the properties of the second largest domain as a function of disorder. We furthermore analysed the effect of disorder on the density of states and showed a transition from hard gap at low disorders to a soft gap at higher disorders. At W = 2, we have analysed the soft gap in detail and found that the density of states deviates slightly (δ ≈ 1.293 ± 0.027) from the linear behaviour in two dimensions. Analysis of local minima show that the pseudo ground states have similar structure.

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Section: Introductionmentioning

confidence: 83%

Effect of increasing disorder on domains of the 2d Coulomb glass

Bhandari¹,

Malik²

2017

J. Phys.: Condens. Matter

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“…1͒. 20,21 This means that the surfaces have a tendency to be ordered "as such," and to see the true ordinary transition behavior, one needs L Ͼ L b . Thus, we use substantially weakened surface interactions J 1 Ӷ J to circumvent this problem.…”

Section: Numerical Resultsmentioning

confidence: 99%

Surface criticality in random field magnets

Laurson

Alava

2005

Phys. Rev. B

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The boundary-induced scaling of three-dimensional random field Ising magnets is investigated close to the bulk critical point by exact combinatorial optimization methods. We measure several exponents describing surface criticality: ␤ 1 for the surface layer magnetization and the surface excess exponents for the magnetization and the specific heat, ␤ s and ␣ s . The latter are related to the bulk phase transition by the same scaling laws as in pure systems, but only with the same violation of the hyperscaling exponent as in the bulk. The boundary disorders faster than the bulk, and the experimental and theoretical implications are discussed.

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“…The study of the exact ground state of the RFIM has been possible due to the existence of a well-established equivalence between the problem of finding the ground state of the Hamiltonian (1) and the problem of finding the cut with minimum capacity of a network [1][2][3]. Using this mapping, many numerical efforts have been devoted to the understanding of how the ground state properties change when the amount of disorder σ is changed for the 2d [4,5] and 3d [6] Gaussian RFIM. In this paper we propose an algorithm that allows us to go one step forward and study the properties of the first excited state (FES) of the Hamiltonian (1).…”

Section: Introductionmentioning

confidence: 99%