Low-energy excitations in the three-dimensional random-field Ising model

Zumsande, Martin; Hartmann, Alexander K.

doi:10.1140/epjb/e2009-00410-2

Cited by 7 publications

(18 citation statements)

References 73 publications

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“…This is because around the transition region many domain wall rearrangements are possible (with very small energy difference) leading to high number of excitations. Such a situation was also observed in 3d RFIM [45]. At higher disorders spin orientation are dominated by the {φ i }, which is fixed for all configurations at each W here.…”

Section: Density Of Statessupporting

confidence: 76%

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: Density Of Statessupporting

confidence: 76%

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

Bhandari¹,

Malik²

2017

J. Phys.: Condens. Matter

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“…Such excitations have been studied in d = 3 so far. 30 Hence, for each realization {hε i } of the disorder, we obtained seven different (ground-state) configurations for different types of boundary conditions/constraints [PBC, (++), (−−), (+−), (−+), bulk-induced droplets, and singlespin-induced droplets]. Technically, to obtain the droplets, we extracted the absolute differences between the spin configuration of two or more GSs via linear combinations of the configurations.…”

Section: Domain Walls and Droplet Excitationsmentioning

confidence: 99%

“…Instead, for the third approach, we follow the arguments of Ref. 30. Therein, it is shown that the distribution of single-spin-induced droplet radii scales as p(R) ∼ R −θ .…”

Section: Domain Walls and Droplet Excitationsmentioning

confidence: 99%

“…Droplet-type low-or lowest-energy excitations have only been obtained in three dimensions so far. 12,30 For three dimensions at finite temperature, also free-energy barriers were calculated recently. 31,32 Furthermore, the prediction for the RFIM upper critical dimension d u = 6 was confirmed 13 via exhaustive exact GS calculation up to d = 7.…”

Section: Introductionmentioning

confidence: 99%

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Excitations in high-dimensional random-field Ising magnets

Ahrens

Hartmann

2012

Phys. Rev. B

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Domain walls and droplet-like excitation of the random-field Ising magnet are studied in d={3,4,5,6,7} dimensions by means of exact numerical ground-state calculations. They are obtained using the established mapping to the graph-theoretical maximum-flow problem. This allows to study large system sizes of more than five million spins in exact thermal equilibrium. All simulations are carried out at the critical point for the strength h of the random fields, h=h_c(d), respectively. Using finite-size scaling, energetic and geometric properties like stiffness exponents and fractal dimensions are calculated. Using these results, we test (hyper) scaling relations, which seem to be fulfilled below the upper critical dimension d_u=6. Also, for d

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“…p = 1/N was chosen since it is the percolation threshold, i.e., the graph is a forest like structure and to form a cycle almost surely non existent edges, i.e., distance 2, need to be used. Like other studies on the solution space structure of different optimization problems, we look at excitations [34][35][36]. To detect signatures of RSB, we use a criterion introduced in the context of TSP by Mézard and Parisi in Ref.…”

Section: Introductionmentioning

confidence: 99%

Replica symmetry and replica symmetry breaking for the traveling salesperson problem

2019

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We study the energy landscape of the Traveling Salesperson problem (TSP) using exact ground states and a novel linear programming approach to generate excited states. We look at some different ensembles, notably the classic finite dimensional Euclidean TSP and the mean-field (1, 2)-TSP, which has its origin directly in the mapping of the Hamiltonian circuit problem on the TSP. Our data supports previous conjectures that the Euclidean TSP does not show signatures of replica symmetry breaking neither in two nor in higher dimension. On the other hand the (1,2)-TSP exhibits a signature of broken replica symmetry.

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Low-energy excitations in the three-dimensional random-field Ising model

Cited by 7 publications

References 73 publications

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

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

Excitations in high-dimensional random-field Ising magnets

Replica symmetry and replica symmetry breaking for the traveling salesperson problem

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