Correlation Functions and the Coexistence of Phases

作者: Michael E. Fisher

DOI: 10.1063/1.1704706

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摘要: We discuss the existence, continuity and other properties of canonical grand many‐particle correlation functions ns(r1, … rs) in thermodynamic limit classical quantum mechanical systems.If pressure system for fixed T is constant range specific volume va to vb, one expects physically observe coexistence two separated phases. In terms this expressed by ns(v)=xa(va/v)ns(va)+xb(vb/v)ns(vb), where x xb are mole fractions phases so that v = xava + xbvb. With aid various lemmas on convex we prove such a ``separation phases'' follows rigorously from statistical mechanics provided ``well defined'' an appropriate sense.

参考文章(8)
R. Peierls, On a Minimum Property of the Free Energy Physical Review. ,vol. 54, pp. 918- 919 ,(1938) , 10.1103/PHYSREV.54.918
J. L. Lebowitz, J. K. Percus, Statistical Thermodynamics of Nonuniform Fluids Journal of Mathematical Physics. ,vol. 4, pp. 116- 123 ,(1963) , 10.1063/1.1703877
Michael E. Fisher, John Stephenson, Statistical Mechanics of Dimers on a Plane Lattice. II. Dimer Correlations and Monomers Physical Review. ,vol. 132, pp. 1411- 1431 ,(1963) , 10.1103/PHYSREV.132.1411
Jean Ginibre, Reduced Density Matrices of Quantum Gases. I. Limit of Infinite Volume Journal of Mathematical Physics. ,vol. 6, pp. 238- 251 ,(1965) , 10.1063/1.1704275
G. E. Uhlenbeck, P. C. Hemmer, M. Kac, On the van der Waals Theory of the Vapor‐Liquid Equilibrium. II. Discussion of the Distribution Functions Journal of Mathematical Physics. ,vol. 4, pp. 229- 247 ,(1963) , 10.1063/1.1703947
Robert B. Griffiths, A Proof that the Free Energy of a Spin System is Extensive Journal of Mathematical Physics. ,vol. 5, pp. 1215- 1222 ,(1964) , 10.1063/1.1704228
Michael E. Fisher, The free energy of a macroscopic system Archive for Rational Mechanics and Analysis. ,vol. 17, pp. 377- 410 ,(1964) , 10.1007/BF00250473
D. Ruelle, Correlation Functionals Journal of Mathematical Physics. ,vol. 6, pp. 201- 220 ,(1965) , 10.1063/1.1704272