Critical phenomena at perfect and non-perfect surfaces

Pleimling, Michel; Selke, W.

doi:10.1007/s100510050198

Cited by 62 publications

(99 citation statements)

References 88 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: 69%

“…Kaneyoshi observed that the critical coupling ratio r sp is shifted to higher values in systems with a diluted surface and he conjectured that this is a common effect of surface amorphisation. This was confirmed by a Monte Carlo study [8] where the strength of surface bonds was chosen randomly between two different values J s1 and J s2 , the ratio d = J s1 /J s2 measuring the degree of dilution. For d = 1/10 the special transition point is located at the mean coupling ratio r sp = 1.7(0.1) for the simple cubic lattice, noticeably larger than the value obtained for the perfect surface r sp ≈ 1.5, see Section 2.1.…”

Section: Semi-infinite Systems With Surface Imperfectionsmentioning

confidence: 78%

“…Recently, new field-theoretical estimates also resulted in negative values for α 11 [43,44]. The Monte Carlo results obtained for three-dimensional semi-infinite Ising models with random surface-bond disorder [8] are also compatibel with the irrelevance of random surface enhancement for the special transition point critical behaviour. However, as short-range random surface enhancement is close to being relevant, one might expect long-range correlated enhancement disorder to be relevant at the special transition point [227].…”

Section: Semi-infinite Systems With Surface Imperfectionsmentioning

confidence: 91%

“…Examples of order parameter profiles obtained by Monte Carlo simulations of threedimensional Ising films with L = 80 layers at temperatures below the bulk critical temperature k B T c /J b = 4.5115 are shown in Figure 1 [8]. Here, all the couplings involved have been chosen to have equal strength J b and no magnetic fields have been retained.…”

Section: Surface Quantities and Phase Diagramsmentioning

confidence: 99%

“…For surface couplings exceeding the bulk couplings by a large amount, magnetisation profiles decreasing monotonically towards the center of the system may also be observed. After [8].…”

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: 69%

Section: Semi-infinite Systems With Surface Imperfectionsmentioning

confidence: 78%

Section: Semi-infinite Systems With Surface Imperfectionsmentioning

confidence: 91%

Section: Surface Quantities and Phase Diagramsmentioning

confidence: 99%

“…For surface couplings exceeding the bulk couplings by a large amount, magnetisation profiles decreasing monotonically towards the center of the system may also be observed. After [8].…”

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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Thermodynamics of holographic defects

Wapler

2010

J. High Energ. Phys.

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Using the AdS/CFT correspondence, we study the thermodynamic properties and the phase diagram of matter fields on (2+1)-dimensional defects coupled to a (3+1)dimensional N = 4 SYM "heat bath". Considering a background magnetic field, (net) quark density, defect "magnitude" δN c and the mass of the matter, we study the defect contribution to the thermodynamic potentials and their first and second derivatives to map the phases and study their physical properties. We find some features that are qualitatively similar to other systems e.g. in (3+1) dimensions and a number of features that are particular to the defect nature, such as its magnetic properties, unexpected properties at T → 0 and finite density; and the finite δN c effects, e.g. a diverging susceptibility and vanishing density of states at small temperatures, a physically consistent negative heat capacity and new types of consistent phases. tities of the full (defect+bulk) field theory that are extrinsic in the area of the defect. Certainly, we will miss contributions that are extrinsic in the volume of the SYM, but these depend only on a "topological" parameter that is related to a difference in the level -2 -J T quantum critical point "ordered" quantum critical phase transition "Higgs" quantum critical phase / J s / J b T J bs u r f a c e t r a n s i t i o n extraordinary transition ordinary transition bulk + boundary "ordered" boundary "ordered" special point

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Critical behaviour of three-dimensional Ising ferromagnets at imperfect surfaces: Bounds on the surface critical exponent

Diehl¹

1998

Eur. Phys. J. B

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The critical behaviour of three-dimensional semi-infinite Ising ferromagnets at planar surfaces with (i) random surfacebond disorder or (ii) a terrace of monatomic height and macroscopic size is considered. The Griffiths-Kelly-Sherman correlation inequalities are shown to impose constraints on the order-parameter density at the surface, which yield upper and lower bounds for the surface critical exponent β1. If the surface bonds do not exceed the threshold for supercritical enhancement of the pure system, these bounds force β1 to take the value β In a recent paper Pleimling and Selke (PS) [1] reported the results of a detailed Monte Carlo analysis of the effects of two types of surface imperfections on the surface critical behaviour of d = 3 dimensional semiinfinite Ising models with planar surfaces and ferromagnetic nearest-neighbour (NN) interactions: (i) random surface-bond disorder and (ii) a terrace of monatomic height and macroscopic size on the surface. For type (i), both the ordinary and special transitions were studied. They found that the asymptotic temperature dependence of the disorder-averaged surface magnetization on approaching the bulk critical temperature T c from below could be represented by a power law ∼ |τ | β1 with τ ≡ (T − T c )/T c , where β 1 agreed, within the available numerical accuracy, with the respective values β ord 1 ≃ 0.8 and β sp 1 ≃ 0.2 of the pure system's ordinary and special transitions. For type (ii), where the interaction constants were chosen such that only an ordinary transition could occur, the same value β ord 1 of the perfect system was found for β 1 .Their findings for the case of (i) are in conformity with the relevance/irrelevance criteria of Diehl and Nüsser [2,3] according to which the pure system's surface critical behaviour should be expected to be stable or unstable with respect to short-range correlated random surfacebond disorder depending on whether the surface specific heat C 11 [4] of the pure system remains finite or diverges at the transition. It is fairly well established [5,6] that C 11 approaches a finite constant at the ordinary transition, but has a leading thermal singularity ∼ |τ |at the special transition, where Φ is the surface crossover exponent. In the latter case, the condition for irrelevance, [2,3] seem to work quite well in practice. Yet, from a mathematical point of view, they are rather weak because they are nothing but a necessary (though not sufficient) condition for stability of the pure system's critical behaviour.In this note, I shall employ the Griffiths-Kelly-Sherman (GKS) inequalities [12] to obtain upper and lower bounds on the surface magnetization densities of both types of imperfect systems, bounds that are given by surface magnetizations of analogous systems without such imperfections. Their known asymptotic temperature dependence near T c will then be exploited to obtain restrictions on the surface critical behaviour of the imperfect systems considered. For some cases of interest studied by PS [1], the equality β 1 = β o...

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Critical phenomena at perfect and non-perfect surfaces

Cited by 62 publications

References 88 publications

Critical phenomena at perfect and non-perfect surfaces

Critical phenomena at perfect and non-perfect surfaces

Thermodynamics of holographic defects

Critical behaviour of three-dimensional Ising ferromagnets at imperfect surfaces: Bounds on the surface critical exponent

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