Soluble model of the phase transition of the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>XY</mi></math></span> model

Daniel R. Stump

doi:10.1103/PhysRevD.22.2490

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Soluble model of the phase transition of the $XY$ model

Daniel R. Stump^*

Physics Department, Indiana University, Bloomington, Indiana 47405

^*Present address: Physics Department, Michigan State University, East Lansing, Michigan 48824.

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Phys. Rev. D 22, 2490 – Published 15 November, 1980

DOI: https://doi.org/10.1103/PhysRevD.22.2490

Abstract

A model that resembles the time-continuum $XY$ model is solved. The nature of the phase transition of the soluble model is discussed and shown to be analogous to the phase transition of the $XY$ model. A second model, which describes a mixed $XY$ - and Ising-spin interaction, is also discussed.

References (14)

J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973) J. M. Kosterlitz, ibid. 7, 1046 (1974)
J. V. Jose, L. P. Kadanoff, S. Kirkpatrick, and D. R. Nelson, Phys. Rev. B 16, 1217 (1977)
F. J. Wegner, Z. Phys. 206, 465 (1967) V. L. Berezinskii, Zh. Eksp. Teor. Fiz. 59, 907 (1970) [Sov. Phys.-JETP 32, 493 (1970)]
E. Fradkin and L. Susskind, Phys. Rev. D 17, 2637 (1978)
D. R. Stump, Phys. Rev. D 20, 2592 (1979)
C. G. Callan, R. F. Dashen, and D. J. Gross, Phys. Rev. D 17, 2717 (1978)
S. Mandelstam, Phys. Rev. D 19, 2391 (1979)
J. B. Kogut, Rev. Mod. Phys. 51, 659 (1979) R. Savit, ibid. 52, 453 (1980)
[13]
P. Jordan and E. P. Wigner, Z. Phys. 47, 631 (1928) E. Lieb, T. Schultz, and D. Mattis, Ann. Phys. (N.Y.) 16, 407 (1961) A. Luther and I. Peschel, Phys. Rev. B 12, 3908 (1975) A. Luther and D. J. Scalapino, ibid. 16, 1153 (1977)
H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, New York, 1971)
P. Pfeuty, Ann. Phys. (N.Y.) 57, 79 (1970)
C. J. Hamer, J. B. Kogut, and L. Susskind, Phys. Rev. Lett. 41, 1337 (1978)
E. Fradkin and S. Raby, Phys. Rev. D 20, 2566 (1979)

[c1] J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973) J. M. Kosterlitz, ibid. 7, 1046 (1974)

[c2] J. V. Jose, L. P. Kadanoff, S. Kirkpatrick, and D. R. Nelson, Phys. Rev. B 16, 1217 (1977)

[c3] F. J. Wegner, Z. Phys. 206, 465 (1967) V. L. Berezinskii, Zh. Eksp. Teor. Fiz. 59, 907 (1970) [Sov. Phys.-JETP 32, 493 (1970)]

[c4] E. Fradkin and L. Susskind, Phys. Rev. D 17, 2637 (1978)

[c5] D. R. Stump, Phys. Rev. D 20, 2592 (1979)

[c6] C. G. Callan, R. F. Dashen, and D. J. Gross, Phys. Rev. D 17, 2717 (1978)

[c7] S. Mandelstam, Phys. Rev. D 19, 2391 (1979)

[c8] J. B. Kogut, Rev. Mod. Phys. 51, 659 (1979) R. Savit, ibid. 52, 453 (1980)

[c9] [13]

[c10] P. Jordan and E. P. Wigner, Z. Phys. 47, 631 (1928) E. Lieb, T. Schultz, and D. Mattis, Ann. Phys. (N.Y.) 16, 407 (1961) A. Luther and I. Peschel, Phys. Rev. B 12, 3908 (1975) A. Luther and D. J. Scalapino, ibid. 16, 1153 (1977)

[c11] H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, New York, 1971)

[c12] P. Pfeuty, Ann. Phys. (N.Y.) 57, 79 (1970)

[c13] C. J. Hamer, J. B. Kogut, and L. Susskind, Phys. Rev. Lett. 41, 1337 (1978)

[c14] E. Fradkin and S. Raby, Phys. Rev. D 20, 2566 (1979)

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Soluble model of the phase transition of the $XY$ model

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Soluble model of the phase transition of the XY model

Abstract

References (14)

Soluble model of the phase transition of the $XY$ model