Study of the three-dimensional Ising model on film geometry with the cluster Monte Carlo method

Ruge, C.; Dunkelmann, S.; Wagner, Friedrich; Wulf, J.

doi:10.1007/bf01052762

Cited by 35 publications

(39 citation statements)

References 23 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 Classessupporting

confidence: 53%

“…If the ratio of the surface coupling J s to the bulk coupling J b , r = J s /J b , is sufficiently small, the system undergoes at the bulk critical temperature T c an ordinary transition, with the bulk and surface ordering occurring at the same temperature. Beyond a critical ratio, r > r sp ≈ 1.50 for the semi-infinite Ising model on the simple cubic lattice [16,17,18], the surface orders at the so-called surface transition at a temperature T s > T c , followed by the extraordinary transition of the bulk at T c . At the critical ratio r sp , one encounters the multicritical special transition point, with critical surface properties deviating from those at the ordinary transition and those at the surface transition.…”

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 Classessupporting

confidence: 53%

Section: Surface Quantities and Phase Diagramsmentioning

confidence: 99%

Critical phenomena at perfect and non-perfect surfaces

Pleimling¹

2004

J. Phys. A: Math. Gen.

100

135

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“…with α ≈ 0.110 [32,33,34] the critical exponent of the specific heat, ∆ ≈ 1.56 [32,33,34] the so-called "gap exponent" which characterizes the bulk equation of state, and ∆ 1 ≈ 0.47 [38,39,40,41] its surface analogue. The scaling functionsf ± , where the signs refer to the sign of t, are discussed in more detail in Refs.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Phase diagram and structure of colloid-polymer mixtures confined between walls

et al. 2006

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The influence of confinement, due to flat parallel structureless walls, on phase separation in colloid-polymer mixtures, is investigated by means of grand-canonical Monte Carlo simulations. Ultra-thin films, with thicknesses between D = 3 − 10 colloid diameters, are studied. The AsakuraOosawa model [J. Chem. Phys. 22, 1255(1954] is used to describe the particle interactions. To simulate efficiently, a "cluster move" [J. Chem. Phys. 121, 3253 (2004)] is used in conjunction with successive umbrella sampling [J. Chem. Phys. 120, 10925 (2004)]. These techniques, when combined with finite size scaling, enable an accurate determination of the unmixing binodal. Our results show that the critical behavior of the confined mixture is described by "effective" critical exponents, which gradually develop from values near those of the two-dimensional Ising model, to those of the three-dimensional Ising model, as D increases. The scaling predictions of Fisher and Nakanishi [J. Chem. Phys. 75, 5875 (1981)] for the shift of the critical point are compatible with our simulation results. Surprisingly, however, the colloid packing fraction at criticality approaches its bulk (D → ∞) value non-monotonically, as D is increased. Far from the critical point, our results are compatible with the simple Kelvin equation, implying a shift of order 1/D in the coexistence colloid chemical potential. We also present density profiles and pair distribution functions for a number of state points on the binodal, and the influence of the colloid-wall interaction is studied.

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“…The 1/L d C in the Swendsen Wang algorithm translates into 1/s for a single cluster algorithm [23] soĝ…”

Section: B the Improved Estimatormentioning

confidence: 99%

Correlation function in Ising models

Ruge

Zhu²,

Wagner

1994

Physica A: Statistical Mechanics and its Applications

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We simulated the fourier transform of the correlation function of the Ising model in two and three dimensions using a single cluster algorithm with improved estimators. The simulations are in agreement with series expansion and the available exact results in d = 2, which shows, that the cluster algorithm can succesfully be applied for correlations. We show as a further result that our data do not support a hypothesis of Fisher that in any d = 2 lattice the fourier transform of the correlation function depends on the lattice generating function only. In d = 3 our simulation are again in agreement with the results from the series expansion, except for the amplitudes f ± , where we find f + /f − = 2.06(1).

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Study of the three-dimensional Ising model on film geometry with the cluster Monte Carlo method

Cited by 35 publications

References 23 publications

Critical phenomena at perfect and non-perfect surfaces

Critical phenomena at perfect and non-perfect surfaces

Phase diagram and structure of colloid-polymer mixtures confined between walls

Correlation function in Ising models

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