TY - JOUR

T1 - Gaussian core model phase diagram and pair correlations in high Euclidean dimensions

AU - Zachary, Chase E.

AU - Stillinger, Frank H.

AU - Torquato, Salvatore

N1 - Funding Information:
We thank Henry Cohn for very useful discussions. S. T. thanks the Institute for Advanced Study for their hospitality during his stay there This work was supported by the Office of Basic Energy Sciences, U.S. Department of Energy under Grant No. DE-FG02-04-ER46108.

PY - 2008

Y1 - 2008

N2 - The physical properties of a classical many-particle system with interactions given by a repulsive Gaussian pair potential are extended to arbitrarily high Euclidean dimensions. The goals of this paper are to characterize the behavior of the pair correlation function g2 in various density regimes and to understand the phase properties of the Gaussian core model (GCM) as parametrized by dimension d. To this end, we explore the fluid (dilute and dense) and crystalline solid phases. For the dilute regime of the fluid phase, a cluster expansion of g2 in reciprocal temperature Β is presented, the coefficients of which may be evaluated analytically due to the nature of the Gaussian potential. We present preliminary results concerning the convergence properties of this expansion. The analytical cluster expansion is related to numerical approximations for g2 in the dense fluid regime by utilizing hypernetted chain, Percus-Yevick, and mean-field closures to the Ornstein-Zernike equation. Based on the results of these comparisons, we provide evidence in support of a decorrelation principle for the GCM in high Euclidean dimensions. In the solid phase, we consider the behavior of the freezing temperature Tf(ρ) in the limit ρ →+∞ and show Tf(ρ) →0 in this limit for any d via a collective coordinate argument. Duality relations with respect to the energies of a lattice and its dual are then discussed, and these relations aid in the Maxwell double-tangent construction of phase coexistence regions between dual lattices based on lattice summation energies. The results from this analysis are used to draw conclusions about the ground-state structures of the GCM for a given dimension.

AB - The physical properties of a classical many-particle system with interactions given by a repulsive Gaussian pair potential are extended to arbitrarily high Euclidean dimensions. The goals of this paper are to characterize the behavior of the pair correlation function g2 in various density regimes and to understand the phase properties of the Gaussian core model (GCM) as parametrized by dimension d. To this end, we explore the fluid (dilute and dense) and crystalline solid phases. For the dilute regime of the fluid phase, a cluster expansion of g2 in reciprocal temperature Β is presented, the coefficients of which may be evaluated analytically due to the nature of the Gaussian potential. We present preliminary results concerning the convergence properties of this expansion. The analytical cluster expansion is related to numerical approximations for g2 in the dense fluid regime by utilizing hypernetted chain, Percus-Yevick, and mean-field closures to the Ornstein-Zernike equation. Based on the results of these comparisons, we provide evidence in support of a decorrelation principle for the GCM in high Euclidean dimensions. In the solid phase, we consider the behavior of the freezing temperature Tf(ρ) in the limit ρ →+∞ and show Tf(ρ) →0 in this limit for any d via a collective coordinate argument. Duality relations with respect to the energies of a lattice and its dual are then discussed, and these relations aid in the Maxwell double-tangent construction of phase coexistence regions between dual lattices based on lattice summation energies. The results from this analysis are used to draw conclusions about the ground-state structures of the GCM for a given dimension.

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U2 - 10.1063/1.2928843

DO - 10.1063/1.2928843

M3 - Article

C2 - 18554027

AN - SCOPUS:45149135013

VL - 128

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 22

M1 - 224505

ER -