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• W2021105003 abstract "A new cell model for classical particle systems is presented and analyzed. In this model the particles are confined to congruent, interconnected, cubic cells of volume ω centered on the points of a cubic lattice with lattice spacing 1/γ. The particles interact via a 2-body potential of the form q(r) + ω−1K(γr). The paper deals with the limiting form of this model in which the cells are very large but their separation is much larger. The free energy density is defined by a(ρ,T)≡lim lim ω→∞lim lim γ→0ã(ρ,T,γ,ω),where ã(ρ, T, γ, ω) is the free energy density at density ρ, temperature T, and arbitrary γ and ω. For a very general class of functions q and K, it is proved that a(ρ, T) is given by a variational principle. For a certain class of functions K (including K ≤ 0), a(ρ, T) is given by the Lebowitz-Penrose generalization of the van der Waals-Maxwell theory. For a different class of functions K the system has crystalline states. When K is chosen so that only particles in nearest-neighbor cells interact and K is isotropic, it is proved that the most general crystalline state of the system has a density distribution with two values ρ+ and ρ− arranged in a checkerboard (sodium chloride) pattern. For the special case with K repulsive, K(0) = 0 and q = 0, the system has a second-order melting transition from a crystalline to a fluid state, with no critical temperature. Various correlation functions are defined and evaluated. In the 1-dimensional nearest-neighbor case, the results include exact versions of the Ornstein-Zernike theory for both fluid and crystalline states. Magnetic systems are also considered. Different special cases of the model yield precisely the Weiss theory of ferromagnetism and the Néel-van Vleck theory of antiferromagnetism." @default.
• W2021105003 created "2016-06-24" @default.
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• W2021105003 date "1971-05-01" @default.
• W2021105003 modified "2023-09-26" @default.
• W2021105003 title "Exactly Solvable Cell Model with a Melting Transition" @default.
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• W2021105003 doi "https://doi.org/10.1063/1.1665645" @default.
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