Finite-size behavior of the simple-cubic Ising lattice

Landau, D. P.

doi:10.1103/physrevb.14.255

Cited by 169 publications

(49 citation statements)

References 18 publications

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“…films with free boundaries, as is well known [103][104][105][106] . We also expect in this case a simple exponential decay of the spin correlation function in the axial direction of the cylinder, analogous to Eq.…”

Section: B Ising Cylinders Without Surface Fieldsmentioning

confidence: 86%

Capillary condensation in cylindrical pores: Monte Carlo study of the interplay of surface and finite size effects

Winkler

Wilms

Virnau

et al. 2010

The Journal of Chemical Physics

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When a fluid that undergoes a vapor to liquid transition in the bulk is confined to a long cylindrical pore, the phase transition is shifted (mostly due to surface effects at the walls of the pore) and rounded (due to finite size effects). The nature of the phase coexistence at the transition depends on the length of the pore: For very long pores the system is axially homogeneous at low temperatures. At the chemical potential where the transition takes place fluctuations occur between vapor-like and liquid-like states of the cylinder as a whole. At somewhat higher temperatures (but still far below bulk criticality) the system at phase coexistence is in an axially inhomogeneous multi-domain state, where long cylindrical liquid-like and vapor-like domains alternate. Using Monte Carlo simulations for the Ising/lattice gas model and the Asakura-Oosawa model of colloid-polymer mixtures the transition between these two different scenarios is characterized. It is shown that the density distribution changes gradually from a double-peak structure to a triple-peak shape, and the correlation length in axial direction (measuring the equilibrium domain length) becomes much smaller than the cylinder length. The (rounded) transition to the disordered phase of the fluid occurs when the axial correlation length has decreased to a value comparable to the cylinder diameter. It is also suggested that adsorption hysteresis vanishes when the transition from the simple domain state to the multi-domain state of the cylindrical pore occurs. We predict that the difference between the pore critical temperature and the hysteresis critical temperature should increase logarithmically with the length of the pore.

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Section: B Ising Cylinders Without Surface Fieldsmentioning

confidence: 86%

Capillary condensation in cylindrical pores: Monte Carlo study of the interplay of surface and finite size effects

Winkler

Wilms

Virnau

et al. 2010

The Journal of Chemical Physics

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“…Studies to reproduce average properties of such small clusters of atoms have been performed. These include several Monte Carlo investigations (see, e.g., [174,175,176]). Critical phenomena at edges in three-dimensional models have, however, been addressed only rarely.…”

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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“…Note that due to finite size effects, the peak is flattened and moved to the right. Our interest is to look for such a transition point and investigate the critical phenomena associated with the transition using finite-size scaling method [14,15,16] …”

Section: Resultsmentioning

confidence: 99%

“…For this purpose, we extract the critical exponents, which are related to specific heat, the order parameter, and the susceptibility, from our simulation data at T c (∞) by using finite-size analysis [14,15,16].…”

Section: Estimation Of the Critical Exponentsmentioning

confidence: 99%

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Critical behaviour of the ferromagnetic Ising model on a triangular lattice

et al. 2009

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We apply a new updating algorithm scheme to investigate the critical behavior of the twodimensional ferromagnetic Ising model on a triangular lattice with nearest neighbour interactions. The transition is examined by generating accurate data for large lattices with L = 8, 10,12,15,20,25, 30, 40, 50. The spin updating algorithm we employ has the advantages of both metropolis and single-update methods. Our study indicates that the transition to be continuous at Tc = 3.6403(2). A convincing finite-size scaling analysis of the model yield ν = 0.9995(21), β/ν = 0.12400 (18), γ/ν = 1.75223 (22), γ ′ /ν = 1.7555 (22), α/ν = 0.00077(420) (scaling) and α/ν = 0.0010(42)(hyperscaling) respectively. Estimates of present scheme yield accurate estimates for all critical exponents than those obtained with Monte Carlo methods and show an excellent agreement with their well-established predicted values.

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Finite-size behavior of the simple-cubic Ising lattice

Cited by 169 publications

References 18 publications

Capillary condensation in cylindrical pores: Monte Carlo study of the interplay of surface and finite size effects

Capillary condensation in cylindrical pores: Monte Carlo study of the interplay of surface and finite size effects

Critical phenomena at perfect and non-perfect surfaces

Critical behaviour of the ferromagnetic Ising model on a triangular lattice

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