Prog. Theor. Phys. Vol. 18 No. 4 (1957) pp. 357-366
A Lattice Model of Liquid Helium, III
— Equilibrium Properties of Liquid He4 and Mixtures of He4 and He3
Quantum Chemistry Laboratory, Chemistry Department, Kyoto University, Kyoto
(Received June 10, 1957)
The partition function of the lattice model of liquid He4 developed in the preceding papers1), 2) is shown to be derived by determining the form of a universal function of one variable so far as one admits three assumptions previously made. Instead of determining the function by using Kikuchi's approximation as before, the determination is made here by making use of the experimental values of heat capacity at various temperatures under saturated vapour pressure together with two other thermodynamical data at the λ-point. Comparison of the values thus derived with experimental ones is made for various thermodynamical quantities of pure liquid He4 and of mixtures of He4 and He3. The agreements are good, and a consistent explanation of various peculiar properties of this liquid is obtained.
DOI : 10.1143/PTP.18.357
- T. Matsubara and H. Matsuda, Prog. Theor. Phys. 16 (1956), 569[PTP].
- H. Matsuda and T. Matsubara, Prog. Theor. Phys. 17 (1957), 19[PTP].
F. London, Phys. Rev. 54 (1938), 947[APS];
J. Phys. Chem. 43 (1939), 49[CrossRef].
A. Bijl, Physica 7 (1940), 869[CrossRef].
A. Bijl, J. H. de Boer, and A. Michels, Physica 8 (1941), 655[CrossRef].
N. N. Bogoliubov, Izv. Akad. Nauk SSSR, Ser. Fiz. 11 (1947), 77.
N. N. Bogoliubov, and D. N. Zubarev, J. Exper. Theoret. Phys. USSR, 28 (1955), 129; Sov. Phys. 1 (1955), 83.
T. Nishiyama, Prog. Theor. Phys. 8 (1952), 655[PTP]; ibid. 9 (1953), 245[PTP].
- I. Prigogine, Adv. in Phys. 3 (1954), 131.
R. P. Feynman, Phys. Rev. 91 (1953), 1291[APS];
ibid. 91 (1953), 1301[APS];
ibid. 94 (1954), 262[APS].
S. T. Butler and M. H. Friedman, Phys. Rev. 98 (1955), 287[APS].
S. Koide, J. Phys. Soc. Jpn. 11 (1956), 7[JPSJ].
- J. G. Daunt, Adv. in Phys. 1 (1952), 209.
J. J. M. Beenakker and K. W. Taconis, Progress in Low Temperature Physics, North-Holland Publishing Company, Amsterdam (1955), 108.
- J. C. King and H. A. Fairband, Bull. Am. Phys. Soc. (3) 28 (1953), 65.
Citing Article(s) :
Progress of Theoretical Physics Vol. 20 No. 5 (1958) pp. 614-624
Bose-Einstein Lattice Gases Equivalent to the Heisenberg Model of Ferro-, Antiferro- and Ferri-Magnetism
Progress of Theoretical Physics Vol. 46 No. 5 (1971) pp. 1337-1359
Relationship among Exactly Soluble Models of Critical Phenomena. I