Universal Jump in the Superfluid Density of Two-Dimensional Superfluids

David R. Nelson; J. M. Kosterlitz

doi:10.1103/PhysRevLett.39.1201

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Universal Jump in the Superfluid Density of Two-Dimensional Superfluids

David R. Nelson^*

J. M. Kosterlitz

Department of Physics, Harvard University, Cambridge, Massachusetts 02138

Department of Mathematical Physics, University of Birmingham, Birmingham B15 2TT, England

^*Work supported by a Junior Fellowship, Harvard Society of Fellows.

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Phys. Rev. Lett. 39, 1201 – Published 7 November, 1977

DOI: https://doi.org/10.1103/PhysRevLett.39.1201

Abstract

We observe that recent theories of phase transitions in the two-dimensional $XY$ model predict a universal jump in the superfluid density of ${}^{4}{He}$ films as $T_{c}$ is approached from below. Specifically, we find that $\lim_{T \to T_{c}} - ρ_{s} \frac{(T)}{T} = 3.52 \times 10^{- 9}$ g/ ${cm}^{2}$ °K. Analogous results should hold for two-dimensional planar magnets and liquid crystals.

References (23)

V. L. Berezinskii, Zh. Eksp. Teor. Fiz. 59, 907 (1970) [Sov. Phys. JETP 32, 493 (1971)] V. L. Berezinskii, Zh. Eksp. Teor. Fiz. 61, 1144 (1971) [Sov. Phys. JETP 34, 610 (1971).]
J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973)
J. M. Kosterlitz, J. Phys. C 7, 1046 (1974)
J. Zittartz, Z. Phys. 23B, 55, 63 (1976)
A. Luther and D. J. Scalapino, Phys. Rev. B 16, 1153 (1977)
J. V. José, L. P. Kadanoff, S. Kirkpatrick, and D. R. Nelson, Phys. Rev. B 16, 1217 (1977)
P. G. Wiegmann, to be published
P. C. Hohenberg, Phys. Rev. 158, 363 (1967) N. D. Mermin J. Math. Phys. (N.Y.) 8, 1061 (1967)
H. E. Stanley and T. A. Kaplan, Phys. Rev. Lett. 17, 913 (1966) W. J. Camp and J. P. Van Dyke, J. Phys. C 8, 336 (1975)
S. Doniach, Phys. Rev. Lett. 31, 1450 (1973)
R. Narvarro and J. L. de Jongh, Physica (Utrecht) 84B, 229 (1976)
P. G. de Gennes, The Physics of Liquid Crystals (Oxford Univ. Press, London, 1974), p. 111
R. H. Kraichnan, J. Fluid. Mech. 67, 155 (1975)
L. Onsager, Nuovo Cimento Suppl. 6, 279 (1949) R. P. Feynmann, Prog. Low Temp. Phys. 1, (1955)
P. C. Hohenberg and P. C. Martin, Ann. Phys. 34, 291 (1965)
[6]
J. M. Kosterlitz and D. J. Thouless, to be published
K. R. Atkins and I. Rudnick, Prog. Low Temp. Phys. 6, 37 (1970)
B. I. Halperin and P. C. Hohenberg, Phys. Rev. 188, 898 (1969)
D. R. Nelson and R. A. Pelcovits, Phys. Rev. B 16, 2191 (1977)
R. B. Meyer, private communication
B. D. Josephson, Phys. Lett. 21, 608 (1966)
D. C. Licciardello and D. J. Thouless, Phys. Rev. Lett. 35, 1475 (1975)

[c1] V. L. Berezinskii, Zh. Eksp. Teor. Fiz. 59, 907 (1970) [Sov. Phys. JETP 32, 493 (1971)] V. L. Berezinskii, Zh. Eksp. Teor. Fiz. 61, 1144 (1971) [Sov. Phys. JETP 34, 610 (1971).]

[c2] J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973)

[c3] J. M. Kosterlitz, J. Phys. C 7, 1046 (1974)

[c4] J. Zittartz, Z. Phys. 23B, 55, 63 (1976)

[c5] A. Luther and D. J. Scalapino, Phys. Rev. B 16, 1153 (1977)

[c6] J. V. José, L. P. Kadanoff, S. Kirkpatrick, and D. R. Nelson, Phys. Rev. B 16, 1217 (1977)

[c7] P. G. Wiegmann, to be published

[c8] P. C. Hohenberg, Phys. Rev. 158, 363 (1967) N. D. Mermin J. Math. Phys. (N.Y.) 8, 1061 (1967)

[c9] H. E. Stanley and T. A. Kaplan, Phys. Rev. Lett. 17, 913 (1966) W. J. Camp and J. P. Van Dyke, J. Phys. C 8, 336 (1975)

[c10] S. Doniach, Phys. Rev. Lett. 31, 1450 (1973)

[c11] R. Narvarro and J. L. de Jongh, Physica (Utrecht) 84B, 229 (1976)

[c12] P. G. de Gennes, The Physics of Liquid Crystals (Oxford Univ. Press, London, 1974), p. 111

[c13] R. H. Kraichnan, J. Fluid. Mech. 67, 155 (1975)

[c14] L. Onsager, Nuovo Cimento Suppl. 6, 279 (1949) R. P. Feynmann, Prog. Low Temp. Phys. 1, (1955)

[c15] P. C. Hohenberg and P. C. Martin, Ann. Phys. 34, 291 (1965)

[c16] [6]

[c17] J. M. Kosterlitz and D. J. Thouless, to be published

[c18] K. R. Atkins and I. Rudnick, Prog. Low Temp. Phys. 6, 37 (1970)

[c19] B. I. Halperin and P. C. Hohenberg, Phys. Rev. 188, 898 (1969)

[c20] D. R. Nelson and R. A. Pelcovits, Phys. Rev. B 16, 2191 (1977)

[c21] R. B. Meyer, private communication

[c22] B. D. Josephson, Phys. Lett. 21, 608 (1966)

[c23] D. C. Licciardello and D. J. Thouless, Phys. Rev. Lett. 35, 1475 (1975)

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Universal Jump in the Superfluid Density of Two-Dimensional Superfluids

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