Modified Critical Correlations Close to Modulated and Rough Surfaces

Hanke, Andreas; Kardar, Mehran

doi:10.1103/physrevlett.86.4596

Cited by 11 publications

(15 citation statements)

References 32 publications

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“…These results in two dimensions have been interpreted in terms of a scale-dependent distribution of opening angles of the fractal boundary [259]. The same analogy has been evoked in the discussion of the surface critical behaviour of self-affine surfaces in [256,257].…”

Section: Semi-infinite Systems With Surface Imperfectionsmentioning

confidence: 77%

“…Using a perturbative calculation in the deformations in height from a flat surface they showed that the leading power law decay of the correlations is the same as for a flat surface, but with a modulated amplitude reflecting the shape of the surface [256,257].…”

Section: Semi-infinite Systems With Surface Imperfectionsmentioning

confidence: 99%

“…Whereas the different kinds of roughnesses discussed so far have been shown to be (or are supposed to be) irrelevant for the surface critical behaviour at the ordinary transition, this is not always the case. In a recent interesting work, Hanke and Kardar [256,257] showed that self-affine rough surfaces may give rise to novel surface critical behaviour with surface critical exponents different from those of the perfect case. Similar results have previously been obtained in two-dimensional systems with fractal boundaries [258,259] yielding new multifractal boundary exponents.…”

Section: Semi-infinite Systems With Surface Imperfectionsmentioning

confidence: 99%

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Critical phenomena at perfect and non-perfect surfaces

Pleimling¹

2004

J. Phys. A: Math. Gen.

100

135

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Abstract. In the past perfect surfaces have been shown to yield a local critical behaviour that differs from the bulk critical behaviour. On the other hand surface defects, whether they are of natural origin or created artificially, are known to modify local quantities. It is therefore important to clarify whether these defects are relevant or irrelevant for the surface critical behaviour.The purpose of this review is two-fold. In the first part we summarise some of the important results on surface criticality at perfect surfaces. Special attention is thereby paid to new developments as for example the study of surface critical behaviour in systems with competing interactions or of surface critical dynamics. In the second part the effect of surface defects (presence of edges, steps, quenched randomness, lines of adatoms, regular geometric patterns) on local critical behaviour in semi-infinite systems and in thin films is discussed in detail. Whereas most of the defects commonly encountered are shown to be irrelevant, some notable exceptions are highlighted. It is shown furthermore that under certain circumstances non-universal local critical behaviour may be observed at surfaces.

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Section: Semi-infinite Systems With Surface Imperfectionsmentioning

confidence: 77%

Section: Semi-infinite Systems With Surface Imperfectionsmentioning

confidence: 99%

Section: Semi-infinite Systems With Surface Imperfectionsmentioning

confidence: 99%

See 1 more Smart Citation

Critical phenomena at perfect and non-perfect surfaces

Pleimling¹

2004

J. Phys. A: Math. Gen.

100

135

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“…Not surprisingly, surface randomness modifies the critical behavior near the surface [2], yet the common expectation is for the bulk properties to remain intact. In this Letter we show that arbitrarily weak surface disorder destroys long range order in the bulk of a system of continuous symmetry at the arbitrarily low temperature.…”

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confidence: 99%

Destruction of Bulk Ordering by Surface Randomness

Vinokur²

2002

Phys. Rev. Lett.

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We demonstrate that the arbitrarily weak quenched disorder on the surface of a system of continuous symmetry destroys long range order in the bulk, and, instead, quasi-long range order emerges. Correlation functions are calculated exactly for the two-and three-dimensional XY model with surface randomness via the functional renormalization group. Even at strong quenched disorder the three-dimensional XY model possesses topological order. We also determine roughness of a domain wall in the presence of surface disorder. 75.10.Nr, 74.60.Ge, 05.50.+q, 64.60.Ak The arbitrarily weak quenched disorder in the bulk of a system of continuous symmetry destroys long range order inherent to the pure system [1] provided that disorder breaks not only the translational symmetry but also the symmetry with respect to transformations of the order parameter, as e.g. random anisotropy in amorphous magnets does. This fundamental fact governs all the physics of condensed matter and results in a wealth of observed static and dynamics behaviors of real solids.In many cases noticeable disorder presents only at the surface. Not surprisingly, surface randomness modifies the critical behavior near the surface [2], yet the common expectation is for the bulk properties to remain intact. In this Letter we show that arbitrarily weak surface disorder destroys long range order in the bulk of a system of continuous symmetry at the arbitrarily low temperature.The predicted effect occurs in a rich variety of systems. Examples include crystal ordering in solids grown on a disordered substrate, liquid crystals interacting with an inhomogeneous surface, superconducting vortices pinned by surface impurities, etc. There are also many two-dimensional systems with edge randomness, e.g. superconducting films with columnar defects in a part of the film or films with a rough edge [3].The reason as to why surface impurities, however weak, break long range bulk order is that the bulk contributes little to the energy of long-wave Goldstone modes: the surface random energy of long-wave excitations turns out to be greater than the corresponding bulk energy. As a result, the inhomogeneous state becomes favorable energetically. Note that ordering survives in the regions of the size less than the distance of these regions from the surface. In other words, if the distance between the two points is greater than their separation from the surface, the order parameter is different in those points. While long range order breaks down, topological order survives and quasi-long range order emerges. This means that the correlation length is infinite and that the correlation functions obey a slow logarithmic dependence of the distance.An easy way to understand the main result of the Letter is based on Imry-Ma arguments [1,4]. Let us consider a region of size L near the surface and compare the energies of ordered and disordered states of the region. If long range order is broken on the scales of the order of L the loss in the bulk (elastic) energy is E bulk ∼ L D /L 2 , where ...

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“…In a previous Letter [30], we showed that the shape of the surface has a distinct influence on the properties of an adjacent medium with long-range correlations. Here we demonstrate this in more detail for two-point correlation functions near a critical point of the medium, for both cases (i) and (ii) outlined above.…”

Section: Introductionmentioning

confidence: 99%

Correlation functions near modulated and rough surfaces

Hanke

Kardar

2002

Phys. Rev. E

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In a system with long-ranged correlations, the behavior of correlation functions is sensitive to the presence of a boundary. We show that surface deformations strongly modify this behavior as compared to a flat surface.The modified near surface correlations can be measured by scattering probes.To determine these correlations, we develop a perturbative calculation in the deformations in height from a flat surface. Detailed results are given for a regularly patterned surface, as well as for a self-affinely rough surface with roughness exponent ζ. By combining this perturbative calculation in height deformations with the field-theoretic renormalization group approach, we also estimate the values of critical exponents governing the behavior of the decay of correlation functions near a self-affinely rough surface. We find that for the interacting theory, a large enough ζ can lead to novel surface critical behavior.We also provide scaling relations between roughness induced critical exponents for thermodynamic surface quantities.

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Modified Critical Correlations Close to Modulated and Rough Surfaces

Cited by 11 publications

References 32 publications

Critical phenomena at perfect and non-perfect surfaces

Critical phenomena at perfect and non-perfect surfaces

Destruction of Bulk Ordering by Surface Randomness

Correlation functions near modulated and rough surfaces

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