Cameo Roles:

Goldschmidt, Nora

doi:10.2307/j.ctt1z27gqg.10

Cited by 2 publications

(5 citation statements)

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“…A curious result of the above analysis is the generic disappearance of the glass order (as reflected by superroughening and/or disordered domain structures) upon the introduction of repulsive interactions. Such glass order was found previously for a single line array in random media using the replica-symmetric RG method [1,4,5], but was absent in more recent studies using a variational method with replica-symmetry breaking (RSB) [7,8]. The latter, which finds instead the ML phase, appears naively consistent with our findings.…”

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confidence: 92%

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Interacting Arrays of Lines and Steps in Random Media

Kierfeld

Hwa

1996

Phys. Rev. Lett.

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The phase diagram of two interacting planar arrays of directed lines in random media is obtained by a renormalization group analysis. The results are discussed in the contexts of the roughening of reconstructed crystal surfaces, and the pinning of flux line arrays in layered superconductors. Among the findings are a glassy flat phase with disordered domain structures, a novel second-order phase transition with continuously varying critical exponents, and the generic disappearance of the glassy "super-rough" phases found previously for a single array. Two kinds of (3x1) microfacets on a (2x1) reconstructed crystal surface. The background (2x1) facets can be on four possible sublattices (marked "a"-"d"). Each (3x1) facet shifts the phase by one sublattice.In this article, we study the effect of point disorders on two interacting species of lines in planar arrays. This problem arises in the study of anisotropically (2x1) reconstructed gold (110) surfaces [12], where two kinds of (3x1) microfacets can be treated as two species of interacting lines [ Fig. 1]. Previous studies of the pure system have revealed a rich phase diagram with a variety of possible phases as a function of the interaction parameters [12,13]. The inclusion of point disorders, say crystalline defects originating from a disordered underlying substrate, induces deformations in the trajectories of the microfacets. Similar issues arise in two layers of magnetically interacting Josephson vortex lines. Performing a renormalization group (RG) analysis in replica space, we are able to obtain a complete picture of the RG-flow. The result is applied to discuss the rich phase diagrams of the anisotropically (2x1) reconstructed crystal surfaces. We also discuss the structure of the glass phases obtained for two planar vortex arrays, and comment on the relevance of our results to the issue of replica-symmetry breaking in a single vortex array.A single species of directed lines confined in a plane containing quenched randomness can be described by the continuum Hamiltonian [2,3] on length scales exceeding the line spacing l. The first part of (1) gives the elastic energy of the line array in terms of a displacement-like scalar field φ(r) (a displacement by l corresponds to a shift of 2π in φ), characterized by an (isotropized) elastic constant K [14]. The second term describes density variations ρ(φ, r) induced by a random potential V (r). The density field has the form ρ(φ(r), r), where ρ 0 = 1/l is the average line density, and r = (x, z) with z along the line direction. The random potential is taken to have zero mean with short-range correlations V (r)V (r ′ ) = gδ 2 (r − r ′ ) of (bare) strength g. An interaction between two such species of lines in the form of r1,r2 V int (r 1 − r 2 )ρ(φ 1 , r 1 )ρ(φ 2 , r 2 ) with a shortranged potential V int [15] leads towith µ = r V int (r) and K µ = µ/8π 2 [14]. We assume the disorder potential V i acting on species i to be statistically identical, with the cross-correlations V 1 (r)V 2 (r ′ ) = g µ δ 2 (r − r ′ ) t...

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confidence: 92%

“…It is known that the lines are pinned by point disorders and become "glassy" at low temperature [4]. However, different analytic [4][5][6][7][8] and numerical [9] studies have yielded conflicting results regarding the nature of the glass phase. A subject of debate is the possible breaking of replica-symmetry in the glass-phase [10,11].…”

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confidence: 99%

Interacting Arrays of Lines and Steps in Random Media

Kierfeld

Hwa

1996

Phys. Rev. Lett.

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“…However, the results concerning the correlations for τ > 0 in the glassy phase differ significantly. The RG analysis carried out on the replica Hamiltonian in a replica symmetric way yields correlations (φ(r) − φ(0)) 2 ∝ τ 2 ln 2 r at large length scales r [6,7,8]. The same result is obtained in the dynamical RG calculation [11,12].…”

Section: Introductionsupporting

confidence: 59%

“…Moreover, the results of numerical simulations confirm neither of the analytical predictions [14]. Essentially three analytic approaches have been applied to the problem: (i) After using the replica trick and mapping onto a 2D XY-model with random anisotropy but without vortices [2,5], a renormalization group (RG) calculation [6,7] has been carried out with the replicated Hamiltonian not taking into account the possibility of replica symmetry breaking (RSB). (ii) The replicated Hamiltonian has also been studied by a variational treatment admitting of continuous RSB finding that a one-step breaking is realized [9,10].…”

Section: Introductionmentioning

confidence: 99%

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Replica Symmetry Breaking in Renormalization: Application to the Randomly Pinned Planar Flux Array

Kierfeld

1995

J. Phys. I France

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The randomly pinned planar flux line array is supposed to show a phase transition to a vortex glass phase at low temperatures. This transition has been examined by using a mapping onto a 2D XY-model with random anisotropy but without vortices and applying a renormalization group treatment to the replicated Hamiltonian based on the mapping to a Coulomb gas of vector charges. This renormalization group approach is extended by deriving renormalization group flow equations which take into account the possibility of a one-step replica symmetry breaking. It is shown that the renormalization group flow is unstable with respect to replica asymmetric perturbations and new fixed points with a broken replica symmetry are obtained. Approaching these fixed points the system can optimize its free energy contributions from fluctuations on large length scales; an optimal block size parameter m can be found. Correlation functions for the case of a broken replica symmetry can be calculated. We obtain both correlations diverging as ln r and ln 2 r depending on the choice of m.

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Cited by 2 publications

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Interacting Arrays of Lines and Steps in Random Media

Interacting Arrays of Lines and Steps in Random Media

Replica Symmetry Breaking in Renormalization: Application to the Randomly Pinned Planar Flux Array

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