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22
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84926798991
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Related treatments of the Lindemann criterion using, however, an isotropic estimate such as (2.16) for the tilt modulus, have been presented by A. Houghton and R. A. Pelcovits (unpublished); see also, M. V. Feigel'mann and V. M. Vinokur (unpublished).
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23
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84926798993
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M. A. Moore, Phys. Rev. B (to be published) uses a Lindemann criterion in a different way to estimate the onset of flux lattice melting. Building on work by D. Maki and H. Takayama [, ] and G. Eilenberger [, Phys. Rev., 164, 628, ], he proposes a continuum elastic theory which depends only on the shear modulus and the superfluid density. This elastic free energy, however, appears to lead to a divergent energy when the flux lines are tilted, in contrast with the finite tilt elastic constant predicted by Eq. (2.16). Tilt energies are determined by a superfluid density which vanishes as H -> Hc2 in Moore's theory, rather than by the macroscopic magnetic response as discussed here. The crossover from Moore's description to the one used here occurs at long wavelengths, and can be understood using the nonlocal elastic constants derived by Brandt;
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(1967)
Prog. Theor. Phys.
, vol.46
, pp. 1651
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28
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24044502681
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and references therein. For a related analysis of dimensional crossover in a slab of superfluid helium, see Appendix C of, 21, 1806, V. A. Ambegaokar, B. I. Halperin, D. R. Nelson, E. D. Siggia, Phys. Rev. B
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(1979)
Phys. Rev. B
, vol.13
, pp. 2986
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Hohenberg, P.C.1
Aharony, A.2
Halperin, B.I.3
Siggia, E.D.4
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30
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84926798990
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R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965); R. P. Feynman, Statistical Mechanics (Benjamin, Reading, 1972).
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33
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84926798989
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and (unpublished).
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34
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0346155158
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We note, however, that this issue is not yet settled in the closely related problem of entangled polymer melts, where there may actually be a phase transition as function of the polymerization index N. See
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(1987)
Phys. Rev. Lett.
, vol.59
, pp. 2674
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Kavassalis, T.A.1
Noolandi, J.2
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38
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84926864296
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A very similar situation arises in renormalization-group treatments of d""-dimensional bosons at low temperatures;
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41
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0003705057
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J. E. Mayer and M. G. Mayer, Statistical Mechanics (Wiley, New York, 1977). For a related quantum virial expansion, see, Pergamon, New York, Sec. 9.7.
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(1984)
Statistical Mechanics
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Pathria, R.K.1
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48
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0142013174
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For an example of a translationally disordered system which becomes crystalline with increasing temperature (reentrant melting) for similar reasons, see
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(1983)
Phys. Rev. B
, vol.27
, pp. 2902
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Nelson, D.R.1
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49
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84926864295
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Natterman and Lipowsky (Ref. 38) suggest that the random-field model overestimates the effect of pinning, and argue that a three-dimensional flux lattice is in fact stable to weak pinning.
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50
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84926798988
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Feigel'man and Vinokur, Ref. 22.
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