Corner spontaneous magnetization

Abraham, D. B.; Latrémolière, F. T.

doi:10.1103/physreve.50.r9

Cited by 14 publications

(14 citation statements)

References 10 publications

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“…Other work focused on the temperature behaviour of the local magnetisation in two-dimensional Ising models with various opening angles and lattice types [163,164,165,166]. Up to now a complete solution has only been obtained for the square lattice Ising model with θ = π/2 [167,168,169]. Further studies also investigated the influence of edges in other twodimensional systems.…”

Section: Ordinary Transitionmentioning

confidence: 99%

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: Ordinary Transitionmentioning

confidence: 99%

Critical phenomena at perfect and non-perfect surfaces

Pleimling¹

2004

J. Phys. A: Math. Gen.

100

135

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“…In this case, a conformal transformation relates the critical pair correlation in a sector with opening angle u to the lattice-continuous limit of the exact results of McCoy and Wu for spins on the edge of an infinite cylinder, this time without an arbitrary factor. The corner magnetization exponent, now known exactly for u p͞2 [6], is obtained by applying scaling ideas to the pair function; only its asymptotic behavior is probed. Checking the complete predicted functional form is therefore a far more exacting test, which we amplify by giving precise formulas for the Ising lattice theory, thus allowing a check of the accuracy of the conformal theory as an approximation to the lattice theory.…”

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confidence: 99%

“…For the similar problem where k 2 is replaced by the imaginary wave vector our first solution [6,7] involved the inverse of the singular integral operator Y of Yang [8] which is known not to exist for T , T c because there is a null spectrum. But it turned out that the statisticalmechanical dual of Y was needed, for which the inverse does exist [9].…”

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confidence: 99%

Correlation Functions in a Corner-Shaped Ising Model

Abraham

Latrémolière

1996

Phys. Rev. Lett.

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We obtain exact results at all temperatures for the two-point function of surface spins near the corner of a two-dimensional rectangular Ising ferromagnet; at the critical point, the functional form predicted by conformal theory is recovered. We are also able to calculate exactly a large class of correlation functions involving spins off the surface, and to interpret the results geometrically. [S0031-9007(96)

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“…The ordinary transition of the isotropic N-vector model at an edge has been investigated by Cardy [20] within the framework of mean-field theory, the renormalization group, and ǫ-expansion. Subsequently the two-dimensional wedge (corner geometry) was studied by exact calculations, mainly for Ising models [21], and by conformal mapping at the bulk critical temperature [22]. New edge and corner exponents were found that depend on the opening angle γ of the wedge.…”

Section: Introductionmentioning

confidence: 99%

Critical adsorption and Casimir torque in wedges and at ridges

Palágyi

Dietrich

2004

Phys. Rev. E

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Geometrical structures of confining surfaces profoundly influence the adsorption of fluids upon approaching a critical point Tc in their bulk phase diagram, i.e., for t = (T −Tc)/Tc → ±0. Guided by general scaling considerations, we calculate, within mean-field theory, the temperature dependence of the order parameter profile in a wedge with opening angle γ < π and close to a ridge (γ > π) for T ≷ Tc and in the presence of surface fields. For a suitably defined reduced excess adsorption Γ±(γ, t → ±0) ∼ Γ±(γ)|t| β−2ν we compute the universal amplitudes Γ±(γ), which diverge as Γ±(γ → 0) ∼ 1/γ for small opening angles, vary linearly close to γ = π for γ < π, and increase exponentially for γ → 2π. There is evidence that, within mean-field theory, the ratio Γ+(γ)/Γ−(γ) is independent of γ. We also discuss the critical Casimir torque acting on the sides of the wedge as a function of the opening angle and temperature.

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Corner spontaneous magnetization

Cited by 14 publications

References 10 publications

Critical phenomena at perfect and non-perfect surfaces

Critical phenomena at perfect and non-perfect surfaces

Correlation Functions in a Corner-Shaped Ising Model

Critical adsorption and Casimir torque in wedges and at ridges

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