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Physica A Statistical Mechanics and its Applications

A simple way of understanding some exact results on critical phenomena in non-homogeneous and finite Ising systems II

Ingo Decker, H. H. Hahn

Published Oct 1, 1977• 3 citations
Publisher
DOI
10.1016/0378-4371(77)90138-8

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Conclusion

Philippe Nozières, David Pines

This chapter concludes the study of superfluidity in Bose liquids with a brief summary of the strengths, and of the inadequacies, of the theory. A clear understanding of the static and the long wavelength dynamic properties of an equilibrium Bose liquid, including a microscopic basis for the two-fluid model. Variational calculations of the excitation spectrum of liquid He II, which are in good quantitative agreement with experiment. A satisfactory phenomenological treatment of the interactions between elementary excitations which give rise to various irreversible phenomena. A microscopic theory of the ground state and elementary excitation spectrum of liquid He II; in fact, even the theory of the simple dilute Bose gas has not yet been extended to treat the system at finite temperatures, and under non-equilibrium situations. A clear understanding of a number of "vortex" properties, including the critical current for superfluid flow in thin capillaries.

CRC Press eBooks•Mar 5, 2018•0 citations
The critical behavior of a two-component lattice-gas model (the 1-2 model) in two and three dimensions is investigated by means of standard and nonstandard methods of series analysis on exact series expansions for the thermodynamic properties of the model. The model exhibits a critical line that passes from the Ising critical point at finite temperature to a critical point at zero temperature. In two dimensions the Ising values of the critical exponents found along the critical line and at zero temperature support the expectation that the model lies in the Ising universality class. In three dimensions Ising values of the critical exponents are found away from zero temperature, but near and at zero temperature the series analysis suggests a crossover to non-Ising values of the critical exponents. This would imply that the model belongs to the Ising universality class at nonzero temperatures and to a different universality class at zero temperature---a quite unexpected result. Various possible explanations for this unusual behavior of the series results are discussed.
This chapter concludes the study of superfluidity in Bose liquids with a brief summary of the strengths, and of the inadequacies, of the theory. A clear understanding of the static and the long wavelength dynamic properties of an equilibrium Bose liquid, including a microscopic basis for the two-fluid model. Variational calculations of the excitation spectrum of liquid He II, which are in good quantitative agreement with experiment. A satisfactory phenomenological treatment of the interactions between elementary excitations which give rise to various irreversible phenomena. A microscopic theory of the ground state and elementary excitation spectrum of liquid He II; in fact, even the theory of the simple dilute Bose gas has not yet been extended to treat the system at finite temperatures, and under non-equilibrium situations. A clear understanding of a number of "vortex" properties, including the critical current for superfluid flow in thin capillaries.