Critical parameters for the<i>d</i>=3 Ising model in a film geometry

An introduction into the theory of boundary critical phenomena and the application of the field-theoretical renormalization group method to these is given. The emphasis is on a discussion of surface critical behavior at bulk critical points of magnets, binary alloys, and fluids. Yet a multitude of related phenomena are mentioned. The most important distinct surface universality classes that may occur for a given universality class of bulk critical behavior are described, and the respective boundary conditions of the associated field theories are discussed. The short-distance singularities of the order-parameter profile in the diverse asymptotic regimes are surveyed.Comment: 24 pages, Latex with 2 figures as eps-files and World Scientific stylefile sprocl.sty, minor additions, updates and correction

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“…. 0.25, in reasonable agreement with various Monte Carlo results, [51][52][53] which yielded values in the range 0.19 . .…”

Section: The Special Transitionsupporting

confidence: 88%

The Theory of Boundary Critical Phenomena

Diehl

1997

Int. J. Mod. Phys. B

316

493

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“…As both the bulk and the surface become critical at the special transition point, the responses of the surface to a bulk field as well as to a surface field diverge. The corresponding critical exponents are estimated to be γ It is worth noting that the Lifshitz point surface critical exponent at the special transition point given in Table II agree within the error bars with the estimates 45,6 of the corresponding exponents for the semi-infinite Ising model. The change from Ising to Lifshitz point bulk critical behaviour when κ b −→ κ L b seems to have only a minor impact on the computed surface critical behaviour at the special transition point.…”

supporting

confidence: 65%

Surface critical exponents at a uniaxial Lifshitz point

Pleimling¹

2002

Phys. Rev. B

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Using Monte Carlo techniques, the surface critical behaviour of three-dimensional semi-infinite ANNNI models with different surface orientations with respect to the axis of competing interactions is investigated. Special attention is thereby paid to the surface criticality at the bulk uniaxial Lifshitz point encountered in this model. The presented Monte Carlo results show that the meanfield description of semi-infinite ANNNI models is qualitatively correct. Lifshitz point surface critical exponents at the ordinary transition are found to depend on the surface orientation. At the special transition point, however, no clear dependency of the critical exponents on the surface orientation is revealed. The values of the surface critical exponents presented in this study are the first estimates available beyond mean-field theory.

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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 Classessupporting

confidence: 53%

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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Critical parameters for thed=3 Ising model in a film geometry

Cited by 35 publications

References 28 publications

The Theory of Boundary Critical Phenomena

The Theory of Boundary Critical Phenomena

Surface critical exponents at a uniaxial Lifshitz point

Critical phenomena at perfect and non-perfect surfaces

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