A unified treatment of Ising model magnetizations

Davies, Brian; Peschel, Ingo

doi:10.1002/andp.19975090304

Cited by 11 publications

(7 citation statements)

References 31 publications

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“…The corner shape, which is scale invariant, leads to local exponents varying continuously with the opening angle. This marginal local critical behaviour has been indeed observed numerically for different systems (see [4] for a review) and, more recently, analytical results have been obtained for the Ising model [5][6][7][8].…”

Section: Introductionsupporting

confidence: 54%

Percolation and conduction in restricted geometries

Lajkó

Turban²

2000

J. Phys. A: Math. Gen.

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The finite-size scaling behaviour for percolation and conduction is studied in two-dimensional triangular-shaped random resistor networks at the percolation threshold. The numerical simulations are performed using an efficient star-triangle algorithm. The percolation exponents, linked to the critical behaviour at corners, are in good agreement with the conformal results. The conductivity exponent, t ′ = ζ/ν, is found to be independent of the shape of the system. Its value is very close to recent estimates for the surface and bulk conductivity exponents.

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Section: Introductionsupporting

confidence: 54%

Percolation and conduction in restricted geometries

Lajkó

Turban²

2000

J. Phys. A: Math. Gen.

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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].…”

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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“…which is in accordance with equation ( 31) for the Ising model. 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].…”

Section: Ordinary Transitionmentioning

confidence: 99%

Critical phenomena at perfect and non-perfect surfaces

Pleimling

Selke

1998

Eur. Phys. J. B

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The effect of imperfections on surface critical properties is studied for Ising models with nearest-neighbour ferromagnetic couplings on simple cubic lattices. In particular, results of Monte Carlo simulations for flat, perfect surfaces are compared to those for flat surfaces with random, 'weak' or 'strong', interactions between neighbouring spins in the surface layer, and for surfaces with steps of monoatomic height. Surface critical exponents at the ordinary transition, in particular $\beta_1 = 0.80 \pm 0.01$, are found to be robust against these perturbations.Comment: 7 pages, 13 figures, submitted to European Physical Journal

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A unified treatment of Ising model magnetizations

Cited by 11 publications

References 31 publications

Percolation and conduction in restricted geometries

Percolation and conduction in restricted geometries

Critical phenomena at perfect and non-perfect surfaces

Critical phenomena at perfect and non-perfect surfaces

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