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36
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Some progress in the use of nonlinear liquid theories for the calculation of liquid modes is described by
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(1992)
J. Chem. Phys.
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Chen, Z.1
Stratt, R.M.2
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45
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Replicas are a common technique for handling the statistical mechanics of quenched disordered systems: See, for example, edited by R. Balian, R. Maynard, and G. Toulouse (North-Holland, Amsterdam
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(1983)
Ill-Condensed Matter.
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Lubensky, T.C.1
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51
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0003644127
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2nd ed. (Academic, London, Liquid theoretical diagrammatic representations and methods are discussed in, and in H. L. Friedman, A Course in Statistical Mechanics (Prentice Hall, Englewood Cliffs)
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(1986)
Theory of Simple Liquids.
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Hansen, J.P.1
McDonald, I.R.2
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60
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In the original work on thermodynamic perturbation theory precisely these kinds of optimized supplements to mean-field theory were explored, Note though, that our particular implementation has a certain level of overcounting; on dissecting the renormalized bonds one finds that the mean-field theory and the first term in the ring sum have some diagrams in common, a pair of υ bonds going from the root to a single other circle, for example. However, the underlying liquid enters differently in these two places [through the true g(r) in the first case and through a hard-core optimization in the second], so it is not entirely clear how best to subtract out the extra terms—besides which, the reasonably impressive agreement between the present theory and simulation suggests that the errors introduced may be rather small.
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Andersen, H.C.1
Chandler, D.2
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In this paper and much of the suceeding literature on polar fluids [J. P. Hansen and I. R. Mc-Donald (Chap. 12) and H. L. Friedman (Chap. 8) from Ref. 27, for example] Δ and D are used to denote what we call the 1 and 2 angular invariants (respectively).
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(1971)
J. Chem. Phys.
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, pp. 4291
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Wertheim, M.S.1
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62
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85034917182
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In a number of previous MSA studies of band structure, a special symmetry of the relevant potential made at least one of the equations trivial. See Chen and Stratt, Refs. 12 and 14. The symmetry was that the longitudinal (L, or equivalently, σ) and transverse (T, or π) components of the potential [formula omitted] satisfied the condition [formula omitted] While this relation obviously holds for the unrenormalized functions [formula omitted] and [formula omitted] Eq. (2.4), it does necessarily hold for the renormalized versions, [formula omitted] and [formula omitted] If it did, it would imply that [formula omitted] making the transverse potential [formula omitted] outside the core in Eq. (4.9)—leading to a transverse chain sum that was basically the Percus-Yevick hard-sphere correlation function. Unfortunately, this symmetry does not seem to survive the renormalization, so one needs to solve the two integral equations numerically.
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