New method for determination of critical parameters

Ruge, C.; Dunkelmann, S.; Wagner, Friedrich

doi:10.1103/physrevlett.69.2465

Cited by 41 publications

(51 citation statements)

References 11 publications

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“…Similar agreement is also obtained for other O(n) models. From the numerical point of view, the best investigated cases are n = 0 [45,46] and n = 1 (Ising) [47,17,18,48,8], whereas studies for n ≥ 2 are scarce [24,49,50,51]. The rather few experimental determinations of surface critical exponents at the ordinary transition, using for example x-ray scattering at grazing angle, yield values which are found to be compatible with the theoretical estimates [52,53,54,55].…”

Section: The Surface Universality Classesmentioning

confidence: 70%

“…If the ratio of the surface coupling J s to the bulk coupling J b , r = J s /J b , is sufficiently small, the system undergoes at the bulk critical temperature T c an ordinary transition, with the bulk and surface ordering occurring at the same temperature. Beyond a critical ratio, r > r sp ≈ 1.50 for the semi-infinite Ising model on the simple cubic lattice [16,17,18], the surface orders at the so-called surface transition at a temperature T s > T c , followed by the extraordinary transition of the bulk at T c . At the critical ratio r sp , one encounters the multicritical special transition point, with critical surface properties deviating from those at the ordinary transition and those at the surface transition.…”

Section: Surface Quantities and Phase Diagramsmentioning

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: The Surface Universality Classesmentioning

confidence: 70%

Section: Surface Quantities and Phase Diagramsmentioning

confidence: 99%

Critical phenomena at perfect and non-perfect surfaces

Pleimling¹

2004

J. Phys. A: Math. Gen.

100

135

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“…Already the result at this order tracks the profile h(x) of the surface. For example, for ρ = |r − r ′ | → ∞ with z and z ′ fixed, the above results for G 0 and G 1 imply the behavior (see Appendix B) 11) up to terms of order (h/z) 2 and (h/z ′ ) 2 . Thus, the leading power law is the same as for a flat surface, but the amplitude is modulated by the surface deformations in the vicinity of r and r ′ by the dimensionless and universal amplitude…”

Section: Introductionmentioning

confidence: 61%

“…Theoretical predictions for surface criticality have been tested experimentally [5][6][7][8][9] and in simulations [10,11]. In particular, the grazing incidence of x-rays and neutrons [3] has become a standard tool for probing critical behavior near surfaces and interfaces [5][6][7][8].…”

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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“…10,14,15 The phase diagram of the semi-infinite Ising model exhibits a critical ratio at r c Ϸ1.50. 14,16 In the case rϽr c an ''ordinary transition'' occurs, which depends on the bulk critical behavior. At r Ͼr c a surface transition occurs which is independent of the bulk transition, while a so-called ''special transition'' occurs at the multicritical point r c .…”

Section: ͑3͒mentioning

confidence: 99%