Analysis of Kosterlitz-Thouless transition models

Physica D: Nonlinear Phenomena

Volumn 99, Issue 4, 1997, Pages 442-470

  Chorin, Alexandre J ^a   Hald, Ole H ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001002553     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(96)00158-3     Document Type: Article

References (28)

1. M. Abramowitz and I.A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965).
2. J. Akao, Phase transitions and connectivity in three-dimensional vortex equilibria, Ph.D Thesis, Math. Dept., UC, Berkeley (1994).
3. A. Alastuey and F. Cornu, Correlations in the Kosterlitz-Thouless phase of the two-dimensional Coulomb problem, J. Stat. Phys. 66 (1992) 165-231.
4. A. Alastuey and P. Forrester, A testbench for the nested dipole hypothesis of Kosterlitz and Thouless, J. Stat. Phys. 79 (1995) 503-523.
5. V. Ambegaokar, B. Halperin, D. Nelson and E. Siggia, Dynamics of superfluid films, Phys. Rev. B 21 (1980) 1806-1826.
6. D. Amit, Y. Goldschmidt and G. Grinstein, Renormalization group analysis in the 2D Coulomb gas, sine-Gordon theory and XY model, J. Phys. A 13 (1980) 585-620.
7. J.J. Binney, N.J. Dowrick, A.J. Fisher and M.E.J. Newman, The Theory of Critical Phenomena, An Introduction to the Renormalization Group (Oxford University Press, Oxford, 1993).
8. A.J. Chorin, Hairpin removal in vortex interactions II, J. Comput. Phys. 107 (1993) 1-9.
9. A.J. Chorin, Vorticity and Turbulence (Springer, Berlin, 1994).
10. A.J. Chorin, Vortex phase transitions in 2.5 dimensions, J. Stat. Phys. 76 (1994) 835-856.
11. A.J. Chorin and O.H. Hald, Vortex renormalization in three space dimensions, Phys. Rev. B 51 (1995) 11 969-11 972.
12. A.J. Chorin and O.H. Hald, Turbulence and linear response, in preparation.
13. B. Halperin, Statistical mechanics of topological defects, Les Houches 1980 Lecture Notes (North-Holland, Amsterdam, 1981).
14. C. Itzykson and J.M. Drouffe, Statistical Field Theory (Cambridge University Press, Cambridge, 1989).
15. J. Jose, L. Kadanoff, S. Kirkpatrick and D. Nelson, Renormalization, vortices and symmetry breaking in the two-dimensional planar model, Phys. Rev. B 16 (1977) 1217-1241.
16. H. Kleinert, Gauge Fields in Condensed Matter (World Scientific, Singapore, 1989).
17. J. Kosterlitz, The critical properties of the two-dimensional XY model, J. Phys. C 7 (1974) 1046-1060.
18. J. Kosterlitz and D. Thouless, Order, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973) 1181-1203.
19. J. Kosterlitz and D. Thouless, Two-dimensional physics, ed. D. Brewer, Prog. Low Temp. Phys. Vol. 7B (North-Holland, Amsterdam, 1978).
20. P. Lammert, Simple-minded models of condensed matter systems, Ph.D Thesis, Dept. of Physics, UC, Berkeley (1993).
21. F. Lund, A. Reisenegger and C. Utreras, Critical properties of a dilute gas of vortex rings in three dimensions and the λ transition in liquid helium, Phys. Rev. B 41 (1990) 155-161.
22. P. Minnhagen, New renormalization group equations for the Kosterlitz-Thouless transition, Phys. Rev. B 32 (1985) 3088-3101.
23. D. Nelson, Defect mediated phase transitions, in: Phase Transitions and Critical Phenomena, eds. C. Domb and J. Lebowitz, Vol. 7 (Academic Press, London, 1983).
24. A Ramirez, F. Lund and R. Hernandez, Effect of vortex bending in the phase transition mediated by vortex rings in three dimensions and its relation to the λ transition in liquid helium, Phys. Rev. B 47 (1993) 5465-5468.
25. S.R. Shenoy, Vortex loop scaling in the three-dimensional XY ferromagnet, Phys. Rev. B 40 (1989) 5056-5068.
26. E. Whitaker and G. Watson, A Course of Modern Analysis (Cambridge University Press, Cambridge, 1962).
27. G. Williams, Vortex ring model of the superfluid λ transition, Phys. Rev. Lett. 59 (1987) 1926-1929.
28. A. Young, On the theory of phase transitions in the two-dimensional planar spin model, Phys. C 11 (1978) L453-L455.