No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Generalized Ornstein‐Zernike Approach to Critical Phenomena
1.L. S. Ornstein and F. Zernike, Proc. Roy. Acad. Amsterdam 17, 793 (1914);
1.F. Zernike, Proc. Roy. Acad. Amsterdam 18, 1520 (1916).
2.J. D. van der Waals, Die Continuität des Gas‐förmigen und Flüssigen Zustandes (Verlag Johann Ambrosius Barth, Leipzig, 1881).
3.J. Willard Gibbs, The Collected Works of J. Willard Gibbs (Longmans Green and Co. Inc., New York, 1931), Vol. I, p. 44.
4.M. S. Green and J. V. Sengers, Eds. Critical Phenomena: Proceedings of a Conference, Washington, D.C., 1965 (N.B.S. Misc. Publ. 223)
4.(National Bureau of Standards, Washington, D.C., 1966).
5.G. E. Uhlenbeck, Critical Phenomena: Proceedings of a Conference Washington, D.C., 1965, M. S. Green and J. V. Sengers, Eds. (N.B.S. Misc. Publ. 223)
5.(National Bureau of Standards, Washington, D.C., 1966), p. 3.
6.M. S. Green, Cargese Lectures in Theoretical Physics; Statistical Mechanics, B. Jancovici, Ed. (Gordon and Breach Science Publishers, Inc., New York, 1966), p. 59.
6.The ideas on the thermodynamics of critical phenomena of L. Tisza have given much insight into these lectures, as well as the present paper. See L. Tisza, Phase Transformations in Solids, R. Smoluchoeski, Ed. (John Wiley & Sons, Inc., New York, 1957), p. 1;
6.and more extensively in Ann. Phys. (N.Y.) 13, 1 (1961).
7.J. L. Lebowitz and J. K. Percus, J. Math. Phys. 4, 218 (1963).
8.L. Landau and E. M. Lifshitz, Statistical Physics (Addison‐Wesley Publ. Co. Inc., Reading, Mass., 1958), pp. 363, et seq.
9.T. Morita and K. Hiroike, Progr. Theor. Phys. 25, 532 (1961).
10.H. Cramèr, Mathematical Methods of Statistics (Princeton University Press, Princeton, N.J., 1951), pp. 310, et seq.
11.We use the following notation here and in subsequent sections: signifies the coordinates and momenta of a set of ν molecules, signifies the phase‐space volume for the ν molecules. We use the usual set‐theoretic symbols to indicate conditions on summations over sets: the set is properly included in the set proper inclusion or identity, the set consisting of all elements common to and all elements belonging either to or to is defined only when and are disjoint and is then their union, is defined only when and is then the complement of in i is a member of ν means the number of molecules in the set Sometimes we use a set symbol as an exponent of in which case the number of particles in the set is meant. A summation over sets is indicated by the usual summation sign and means summation over all sets satisfying the conditions which appear below the summation sign.
12.J. Willard Gibbs, “Elementary Principles of Statistical Mechanics,” Collected Works of J. Willard Gibbs (Longmans Green and Co., Inc., New York), Vol. II.
13.R. E. Nettleton and M. S. Green, J. Chem. Phys. 29, 1365 (1958).
14.J. K. Percus, Phys. Rev. Letters, 462 (1962);
14.The Equilibrium Theory of Classical Fluids, H. L. Frisch and J. L. Lebowitz, Eds. (W. A. Benjamin, Inc., New York, 1964), Vol. II, pp. 33, et seq.
15.M. E. Fisher, J. Math. Phys. 6, 1643 (1965).
16.R. B. Griffiths has shown (private communication) on the basis of inequalities proved by himself, Kelly and Sherman that for a ferromagnetic Ising system the ratios are bounded above and below;
16.R. B. Griffiths, J. Math. Phys. 8, 478 and (1967).
16.O. G. Kelly and S. Sherman (unpublished).
17.M. S. Green, Lectures in Theoretical Physics, Vol. III, W. E. Britten, B. W. Downs, and J. Downs, Eds. (Interscience Publishers Inc., New York, 1961), p. 195.
Article metrics loading...
Full text loading...