Corner spontaneous magnetization

Abraham, D. B.; Latrémolière, F. T.

doi:10.1007/bf02179247

Cited by 13 publications

(12 citation statements)

References 22 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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“…It turns out that coshg͑k͒ cosh2K ‫ء‬ 1 cosh2K 2 2 sinh2K ‫ء‬ 1 sinh2K 2 cosk (5) and that there is a quantization condition e iMk 2ia͑k͒e id ‫ء‬ ͑k͒ where a͑k͒ 6i, and the function d ‫ء‬ is defined in [7] along with d 0 , w 0 , w 1 and the expression of y m,k . Note that all these functions have a similar analytic structure, with branch points at A 61 , B 61 with A cothK ‫ء‬ 1 cothK 2 and B cothK ‫ء‬ 1 tanhK 2 .…”

mentioning

confidence: 99%

“…Note that all these functions have a similar analytic structure, with branch points at A 61 , B 61 with A cothK ‫ء‬ 1 cothK 2 and B cothK ‫ء‬ 1 tanhK 2 . The appearance of a can be understood by appealing to the reflection invariance of V 0 [7].…”

mentioning

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].…”

mentioning

confidence: 99%

“…The second ingredient in the Wiener-Hopf method of [4,10] as used in [7] is the relationship between opposite values of k which we read from the expression of X y k :…”

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confidence: 99%

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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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A unified treatment of Ising model magnetizations

Davies¹,

Peschel²

1997

Annalen der Physik

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We show how the spontaneous bulk, surface and corner magnetizations in the square lattice Ising model can all be obtained within one approach. The method is based on functional equations which follow from the properties of corner transfer matrices and vertex operators and which can be derived graphically. In all cases, exact analytical expressions for general anisotropy are obtained. Known results, including several for which only numerical computation was previously possible, are verified and new results related to general anisotropy and corner angles are obtained.Comment: Plain Tex, 30 pages, 21 figures in eps format. Revised for publication in Annalen der Physi

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Corner spontaneous magnetization

Cited by 13 publications

References 22 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

A unified treatment of Ising model magnetizations

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