Order-Parameter Distribution Function of Finite<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">O</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">n</mml:mi><mml:mo>)</mml:mo></mml:math>Symmetric Systems

Xs, Chen; Dohm, V.; Schultka, Norbert

doi:10.1103/physrevlett.77.3641

Cited by 37 publications

(53 citation statements)

References 25 publications

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“…In this case, a logarithmic correction factor 81,82 arises in the scaling relation for the Onsager kinetic coefficient L = ͓1 − ͑ln S / /2S / ͔͒, where S is the spacing between the plates. [83][84][85] Based on these observations, a logarithmic correction is not expected in our simulations, which also incorporate periodic boundary conditions. [83][84][85] Based on these observations, a logarithmic correction is not expected in our simulations, which also incorporate periodic boundary conditions.…”

Section: Resultsmentioning

confidence: 65%

Dynamics of fluids near the consolute critical point: A molecular-dynamics study of the Widom–Rowlinson mixture

Jagannathan

Yethiraj

2005

The Journal of Chemical Physics

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Molecular-dynamics simulations are presented for the dynamic behavior of the Widom-Rowlinson mixture [B. Widom, and J. S. Rowlinson, J. Chem. Phys. 52, 1670 (1970)] at its critical point. This model consists of two components where like species do not interact and unlike species interact via a hard-core potential. Critical exponents are obtained from a finite-size scaling analysis. The self-diffusion coefficient shows no anomalous behavior near the critical point. The shear viscosity and thermal conductivity show no divergent behavior for the system sizes considered, although there is a significant critical enhancement. The mutual diffusion coefficient, D(AB), vanishes as D(AB) approximately xi(-1.26 +/- 0.08), where xi is the correlation length. This is different from the renormalization-group (D(AB) approximately xi(-1.065)) mode coupling theory (D(AB) approximately xi(-1)) predictions. The theories and simulations can be reconciled if we assume that logarithmic corrections to scaling are important.

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Section: Resultsmentioning

confidence: 65%

Dynamics of fluids near the consolute critical point: A molecular-dynamics study of the Widom–Rowlinson mixture

Jagannathan

Yethiraj

2005

The Journal of Chemical Physics

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“…Here we point out, however, that such a non-perturbative treatment can be avoided because the exponential size dependence of the ϕ 4 lattice model above T c is not of a truly non-perturbative nature, unlike the effects due to the Goldstone modes below T c [47] . We shall show that an ordinary renormalized perturbation approach is sufficient if one restricts oneself to the region L > ξ above T c .…”

Section: Perturbation Theory Above T Cmentioning

confidence: 97%

“…Covering the size dependence in the entire L −1 − ξ −1 plane, i.e., both at T = T c as well as for L/ξ ≫ 1 at fixed ξ < ∞, would require a non-perturbative treatment [52] within the mode expansion mentioned above. Such a treatment could be given on the basis of the order-parameter distribution function [47] that includes the higher modes in a non-perturbative way.…”

Section: Perturbation Theory Above T Cmentioning

confidence: 99%

Violation of finite-size scaling in three dimensions

Chen

Dohm

1999

Eur. Phys. J. B

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“…The averages are defined as < Φ m >= ∞ −∞ dΦΦ m P (Φ) where P (Φ) = Z −1 Dσe −H is the order-parameter distribution function with σ(x) = ϕ(x) − Φ representing the inhomogeneous fluctuations [12]. From Refs.…”

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confidence: 99%

Finite-Size Effects in the φ⁴ Field and Lattice Theory Above the Upper Critical Dimension

Chen

Dohm

1998

Int. J. Mod. Phys. C

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We demonstrate that the standard O(n) symmetric ϕ 4 field theory does not correctly describe the leading finite-size effects near the critical point of spin systems on a d-dimensional lattice with d > 4. We show that these finite-size effects require a description in terms of a lattice Hamiltonian. For n → ∞ and n = 1 explicit results are given for the susceptibility and for the Binder cumulant. They imply that recent analyses of Monte-Carlo results for the five-dimensional Ising model are not conclusive.PACS numbers: 05.70. Jk, 64.60.Ak, 75.40.Mg The effect of a finite geometry on systems near phase transitions is of basic interest to statistical physics and elementary particle physics. In both areas the ϕ 4 Hamiltonianfor an n-component field ϕ(x) in a finite volume V plays a fundamental role [1]. For simplicity we considerThe summation runs over discrete k vectors with componentsIt is generally believed that the leading finite-size effects near the critical point of d-dimensional systems can be described by H both for d ≤ d u and for d > d u where d u = 4 is the upper critical dimension. Since for d > 4 the bulk critical behavior is mean-field like, it is plausible that the leading finite-size effects for d > 4 appear to be describable in terms of a simplified Hamiltonian [2,3]involving only the homogeneous fluctuations of the low- In this Letter we shall demonstrate that the lowestmode approach fails for the Hamiltonian H in Eq.(1) for d > 4 and that the leading finite-size effects of spin systems on a d-dimensional lattice with d > 4 are not correctly described by H. We show that this defect of H is due to the (▽ϕ) 2 term. These unexpected findings shed new light on the role of lattice effects for d > d u and imply that recent analyses of the MC data [4][5][6][7] in terms of the continuum ϕ 4 theory are not conclusive. We shall prove our claims first in the large-n limit where a saddle point approach [1] can be employed. Our proof is not based on the renormalization group. We have extended the saddle point approach to the finite system to derive the order-parameter correlation functionwith the statistical weight exp(−H). In the limit n → ∞ at fixed u 0 n we have found the exact resultWe shall denote the bulk critical temperature by T c . For T ≥ T c , χ can be interpreted as the susceptibility (per component) of the finite system. In the bulk limit the standard equation [8] for the bulk susceptibility χ b for T ≥ T c is recovered from Eq.(4) aswhere k stands for (2π)It is convenient to rewrite Eq.(4) in terms of r 0 − r 0c = a 0 t where r 0c = −4u 0 n k k −2 is the bulk critical value of r 0 as determined from Eq. (5) δr 0 = a 0 t − ∆,

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Order-Parameter Distribution Function of FiniteO(n)Symmetric Systems

Cited by 37 publications

References 25 publications

Dynamics of fluids near the consolute critical point: A molecular-dynamics study of the Widom–Rowlinson mixture

Dynamics of fluids near the consolute critical point: A molecular-dynamics study of the Widom–Rowlinson mixture

Violation of finite-size scaling in three dimensions

Finite-Size Effects in the φ⁴ Field and Lattice Theory Above the Upper Critical Dimension

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Order-Parameter Distribution Function of FiniteO(n)Symmetric Systems

Cited by 37 publications

References 25 publications

Dynamics of fluids near the consolute critical point: A molecular-dynamics study of the Widom–Rowlinson mixture

Dynamics of fluids near the consolute critical point: A molecular-dynamics study of the Widom–Rowlinson mixture

Violation of finite-size scaling in three dimensions

Finite-Size Effects in the φ4 Field and Lattice Theory Above the Upper Critical Dimension

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Product

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Finite-Size Effects in the φ⁴ Field and Lattice Theory Above the Upper Critical Dimension