Dynamical computer simulations on hard hyperspheres in four- and five-dimensional space

Michels, Jan; Trappeniers, N.J.

doi:10.1016/0375-9601(84)90749-7

Cited by 59 publications

(57 citation statements)

References 4 publications

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“…respectively. Expanding the integral in (7) for z ∼ −z 0 and z ∼ z t one finds that the density terminates at both ends with a square-root singularity. We now consider a general R matrix taking the form…”

Section: Discussionmentioning

confidence: 98%

Critical exponents from cluster coefficients

Rotman

Eisenberg

2009

Phys. Rev. E

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For a large class of repulsive interaction models, the Mayer cluster integrals can be transformed into a tridiagonal real symmetric matrix R_{mn} , whose elements converge to two constants. This allows for an effective extrapolation of the equation of state for these models. Due to a nearby (nonphysical) singularity on the negative real z axis, standard methods (e.g., Padé approximants based on the cluster integrals expansion) fail to capture the behavior of these models near the ordering transition, and, in particular, do not detect the critical point. A recent work [E. Eisenberg and A. Baram, Proc. Natl. Acad. Sci. U.S.A. 104, 5755 (2007)] has shown that the critical exponents sigma and sigma;{'} , characterizing the singularity of the density as a function of the activity, can be exactly calculated if the decay of the R matrix elements to their asymptotic constant follows a 1/n;{2} law. Here we employ renormalization group (RG) arguments to extend this result and analyze cases for which the asymptotic approach of the R matrix elements toward their limiting value is of a more general form. The relevant asymptotic correction terms (in RG sense) are identified, and we then present a corrected exact formula for the critical exponents. We identify the limits of usage of the formula and demonstrate one physical model, which is beyond its range of validity. The formula is validated numerically and then applied to analyze a number of concrete physical models.

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Section: Discussionmentioning

confidence: 98%

Critical exponents from cluster coefficients

Rotman

Eisenberg

2009

Phys. Rev. E

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“…The phase transition freezing (ρ f ) and melting (ρ s ) densities are given in Table 3 for D = 2 [39,42], D = 3 [4,43,44], and D = 4, 5 [38]. We list also the density ρ cp and the scaled density B 2 ρ cp = 2 D−1 η cp of the densest lattices for dimensions D = 2, .…”

Section: Phase Transitionmentioning

confidence: 99%

Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions

2005

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We evaluate the virial coefficients B k for k ≤ 10 for hard spheres in dimensions D = 2, · · · , 8. Virial coefficients with k even are found to be negative when D ≥ 5. This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when D ≥ 5. Further analysis provides evidence that negative virial coefficients will be seen for some k > 10 for D = 4, and there is a distinct possibility that negative virial coefficients will also eventually occur for D = 3.

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“…The data they presented for d =4,5 are confined to a density range that does not include the sign-crossover point. However, it is apparent that the extrapolated zero-RMPE density may in fact overshoot the currently available computer estimates of the freezing density 30,31 by about 18% in four dimensions and, possibly, by even more in five dimensions. Unfortunately, such estimates are not based on the univocal thermodynamic criterion that ͑at a given temperature͒ requires the pressures and chemical potentials of the fluid and solid phases to be equal at coexistence.…”

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confidence: 90%

Comment on “Residual multiparticle entropy does not generally change sign near freezing” [J. Chem. Phys. 128, 161101 (2008)]

Giaquinta

2009

The Journal of Chemical Physics

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Does the vanishing of the residual multiparticle entropy, a quantity defined as the cumulative contribution of more-than-two-particle density correlations to the excess entropy of a fluid, have physical significance? We address this question in the light of the arguments presented in the paper that is being commented on and of the phenomenology thus far explored in a variety of model systems undergoing thermodynamic or structural transformations into more ordered (but not necessarily crystalline) states or regimes.

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Dynamical computer simulations on hard hyperspheres in four- and five-dimensional space

Cited by 59 publications

References 4 publications

Critical exponents from cluster coefficients

Critical exponents from cluster coefficients

Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions

Comment on “Residual multiparticle entropy does not generally change sign near freezing” [J. Chem. Phys. 128, 161101 (2008)]

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