Abstract
We compare the defects in different physical systems, exhibit their relevant properties for phase transitions, and point out the similarity of the lattice field theories by which their ensembles can be studied.
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References
In solids this was noticed in 1952 by W. Shockley in L’Etat Solid, Proc. Neuvieme Conseil de Physique, Brussels, ed. R. Stoops (Institut International du Physique, solvay, Brussels, 1952).
In superfluid He this was proposed by R.P. Feynman in 1955 in Progress in Low Temperature Physics, 1, ed. C.J. Gorter (North-Holland, Amsterdam, 1955) and later by
V.N. Popov, Sov. Phys. JETP 37 341(1973). In two dimensions, the study was performed in detail in He II by
J.M. Kosterlitz and D.J. Thouless, J. Phys. C (Solid State Phys.) 6, 1181 (1973) and by
J.V. Jorgé, L.P. Kadanoff et al., Phys. Rev. B16, 1217 (1977). The two dimensional melting was attempted in complete analogy, by
D.R. Nelson and B.I. Halperin, Phys. Rev. B19, 2457(1979), but these authors mutilated the physical properties of defects by givinq them an unphysical core energy which led to strange phases. For a correct treatment see
H. Kleinert, Phys. Lett. 95A, 381 (1983).
In four dimensional QCD, a similar study was initiated by A. Polyakov et al., Phys. Lett. 59B, 85 (1975) and
G. t’Hooft, Phys. Rev. D14, 3432 (1976) and continued by many others such as C. Callan, R.F. Dashen, and D.J. Gross, see Phys. Rev. Lett. 44D, 435 (1980) and references.
The confinement in 3 dimensional compact QED was realized by A. Polyakov, Phys. Lett. 59B, 82 (1975) and Nucl. Phys. B120, 429 (1977). See also
J.B. Bronzan and Ashok Das, Phys. Rev. D26, 1415 (1982) for a recent study, and
T. Banks, R. Myerson and J. Kogut, Nucl. Phys. B129, 493 (1977).
E. Kröner, Lecture presented at the 1980 Les Houches Summer School on The Physics of Defects, ed. R. Balian (North-Holland, Amsterdam, 1981).
R. de Wit, Journal of Research (Nat. Bur. of Standards-A, Phys. and Chem.), 77A, 49 (1973).
For more details see H. Kleinert, Gauge Theory of Defects and Stresses, Gordon and Breach, 1984.
H. Kleinert, Lett. Nuovo Cimento, 35, 41 (1982).
J.A. Schouten, Ricci-Calculus, Springer, Berlin, 1954.
H. Kleinert, Phys. Lett. A93, 861 (1982).
W. Helfrich, Proc. International Liquid Crystal Conference, Bangalore, Heyden and Son, London, 1980.
H. Kleinert, Phys. Lett. 95A, 381, 493 (1983).
R.G. Bowers and G.S. Joyce, Phys. Lett. 19, 630 (1967), See also
D.D. Bettd in Phase Transitions and Critical Phenomena, Vol 3, eds. C. Domb and M. Green, Academic, New York, 1947.
J. Villain, J. de Physique (Paris), J. Phys. 36, 581 (1975). It is important to notice that the approximation is valid not only for large 3 (where it is obvious with βv-β) but also for small 3. In fact, the phase transition lies at β∼.46, i.e. in the low β regime where ßV ∼- (2log /2 - 2/4 + 5 4/192-...)-1 .33, not in the high β regime where ßv∼ß (1-1/2ß+...). It corresponds to the approximation In (β)/I0(β) ∼ exp(n2log /2) for n = C,+ 1 and small β, rather than In (β)/I0 (β) ∼ exp(-n2/2β) for large β. This was overlooked by
T. Banks, R. Myerson, and J. Kogut, Nucl. Phys. B129, 493 (1979) and many later papers.
H. Kleinert, Phys. Lett. A91, 295 (1982).
H. Kleinert, Lett. Nuovo Cimento 37, 425 (1983).
H. Kleinert, Phys. Lett. A89, 294 (1982), and Lett. Nuovo Cimento 34, 464 (1982).
H. Kleinert, Phys. Lett. A95, 493 (1983).
E. Brezin and J.M. Drouffe, Nucl Phys. B200 FS4, 93 (1982)
J.M. Drouffe, Nucl. Phys. B205, FS5 27 (1982).
J. Greensite and B. Lautrup, Phys. Lett. 104B, 41 (1981).
H. Flyvbjerg, B. Lautrup, and J.B. Zuber, Phys. Lett. 110B, 279 (1982), B. Lautrup, Mean Field Methods in Gauge Theories, Lecture presented at the 13th Symposium on High Energy Physics, Bad Schandau, DDR, 1982.
R. Balian et al., Phys. Rev. D11, 2104 (1975).
S. Ami, T. Hofsäss and R. Horsley, Phys. Lett. 101A, 145 (1984).
L. Jacobs and H. Kleinert, J.Phys. A15, L 361 (1984).
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© 1984 Plenum Press, New York
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Kleinert, H. (1984). Defect Mediated Phase Transitions in Superfluids, Solids, and their Relation to Lattice Gauge Theories. In: ’t Hooft, G., Jaffe, A., Lehmann, H., Mitter, P.K., Singer, I.M., Stora, R. (eds) Progress in Gauge Field Theory. NATO ASI Series, vol 115. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0280-4_12
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DOI: https://doi.org/10.1007/978-1-4757-0280-4_12
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