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Kosterlitz-Thouless Physics

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Statistical Mechanics

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Abstract

In this chapter, we will study how certain kinds of order are destroyed by thermal excitations. We will focus initially on crystals in different dimensions. The simplest excitations are the linear ones, phonons.

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References

  • M. Aizenman, J.M. Chayes, L. Chayes, C.M. Newman, Discontinuity of the magnetization in one-dimensional \(1/|x-y|^2\) Ising and Potts models. J. Stat. Phys. 50, 140 (1988)

    Google Scholar 

  • N.W. Ashcroft, N.D. Mermin, Solid State Physics (Brooks Cole, 1976)

    Google Scholar 

  • P.W. Anderson, G. Yuval, D.R. Hamann, Exact results in the Kondo problem. II. Scaling theory, qualitatively correct solution, and some new results on one-dimensional classical statistical models. Phys. Rev. B1, 4464 (1970)

    Google Scholar 

  • P.W. Anderson, G. Yuval, Some numerical results on the Kondo problem and the inverse square one-dimensional Ising model. J. Phys. C Solid St. Phys. 4, 607 (1971)

    Google Scholar 

  • D.J. Bishop, J.D. Reppy, Study of the superfluid transition in two-dimensional 4He films. Phys. Rev. B 22, 5171 (1980)

    Article  ADS  Google Scholar 

  • R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey, D.E. Knuth, On the Lambert W function. Adv. Comp. Math. 5, 329 (1996)

    Article  MathSciNet  Google Scholar 

  • Y. Imry, L. Gunther, Fluctuations and physical properties of the two-dimensional crystal lattice. Phys. Rev. B 3, 3939 (1971)

    Article  ADS  Google Scholar 

  • J. José, L.P. Kadanoff, S. Kirkpatrick, D.R. Nelson, Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model. Phys. Rev. B16, 1217 (1977); (Erratum) Phys. Rev. B17 1477 (1978)

    Google Scholar 

  • J. Kondo, Resistance minimum in dilute magnetic alloys. Prog. Theor. Phys. 32, 37 (1964)

    Google Scholar 

  • J.M. Kosterlitz, The critical properties of the two-dimensional xy model. J. Phys. C Solid State Phys. 7, 1046 (1974)

    Article  ADS  Google Scholar 

  • J.M. Kosterlitz, Kosterlitz Thouless physics: a review of key issues. Rep. Prog. Phys. 79, 026001 (2016)

    Article  ADS  Google Scholar 

  • J.M. Kosterlitz, D.J. Thouless, Long range order and metastability in two-dimensional solids and superfluids. J. Phys. C Solid State Phys. 5, L124 (1972)

    Article  ADS  Google Scholar 

  • J.M. Kosterlitz, D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C Solid State Phys. 6, 1181 (1973)

    Article  ADS  Google Scholar 

  • N.D. Mermin, Crystalline order in two dimensions. Phys. Rev. 176 (1968)

    Google Scholar 

  • S.A. Solla, E.K. Riedel, Vortex excitations and specific heat of the planar model in two dimensions. Phys. Rev. B 23(6008), 12 (1981)

    Google Scholar 

  • D.J. Thouless, Long range order in one-dimensional Ising systems. Phys. Rev. 187, 732 (1969)

    Article  ADS  Google Scholar 

  • J. Villain, Theory of one-dimensional and two-dimensional magnets with an easy magnetization plane: planar classical two-dimensional magnet. J. Phys. 36, 581 (1975)

    Article  Google Scholar 

  • K.G. Wilson, The renormalization group: critical phenomena and the Kondo problem. Rev. Mod. Phys. 47, 773 (1975)

    Article  ADS  MathSciNet  Google Scholar 

  • A.P. Young, On the theory of the phase transition in the two-dimensional planar spin model. J. Phys. C Solid State Phys. 11, L453 (1978)

    Article  ADS  Google Scholar 

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Correspondence to A. J. Berlinsky .

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Berlinsky, A.J., Harris, A.B. (2019). Kosterlitz-Thouless Physics. In: Statistical Mechanics. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-28187-8_21

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