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1
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84926563993
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For a review, see Proceedings of the NATO Advanced Research Workshop on Coherence in Superconducting Networks, Delft, 1987, edited by J. E. Mooij and G. B. J. Schön [Physica B 142, 1 302 (1988)].
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33
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0001239990
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Theory of one- and two-dimensional magnets with an easy magnetization plane. II. The planar, classical, two-dimensional magnet
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(1975)
Journal de Physique
, vol.36
, pp. 581
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Villain, J.1
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37
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84926545334
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While we expect that the possible thermodynamic states for the cosine and the Villain interactions will be the same, there has been some suggestion that there may be nonuniversal behavior in such models that can result in differing critical exponents for differing interaction potentials; see the work by Lee et al. in Ref. onlinecitehalf.
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52
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84926534788
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Whether Tc is equal to, or slightly lower than, Tm for the f=1/2 model remains a question of some controversy. See Refs. onlinecitehalf,jrl1.
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54
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0024054246
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Uniformly frustrated xy models: Ground state configurations
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31, 5728, for earlier attempts to find this ground state., T. C. Halsey, Phys. Rev. B
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(1985)
Physica B: Condensed Matter
, vol.152
, pp. 30
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Teitel, S.1
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55
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84926585259
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Due to our rescaling of the Coulomb gas temperature by a factor 2π J0 [see discussion following Eq. ( refe4)], the energy barrier in our units is a factor 2π smaller than the value quoted in Ref. onlinecitebarrier for a Josephson array.
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58
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Our estimate for the barrier in the honeycomb network follows the calcuation presented in Ref. onlinecitebarrier. Note that we have cited here energy barriers as computed for Josephson arrays with a cosine interaction between superconducting nodes, while we have made comparison to transition temperatures Tc and Tm for the Villain interaction between nodes. For the cosine interaction, however, the corresponding transitions will occur at lower temperatures than in the Villain case (due to the additional reduction in junction coupling resulting from the vortex spin wave interaction which is present in the cosine model). Thus these transitions will be even more obscured by high energy barriers than our comparison might indicate. Using the same method we have also computed the barriers for the Villain interaction and we have found that for all types of networks these are even much higher (typically by one order of magnitude) than those cited for the cosine model. For example, we have computed EbVillain=0.517 for a square network, at low temperature. This large difference comes predominantly from the bond that is crossed by the vortex when climbing to the neighboring site, and it can be easily understood by comparing Villain and cosine potentials. We note also that, although these barriers are important for the dynamics of real networks, they do not effect the equilibration of our simulation; this is because in our Coulomb gas MC, we move vortices in discrete steps to neighboring cells, without the need to climb over the energy barrier. However, had we done typical Metropolis MC in terms of the phases θi and the Hamiltonian of Eq. ( refeqH), these barriers would cause equilibration problems; this is because when a vortex moves from one cell to its neighbor, the θi evolve along a continuous path in phase space that therefore must take the system over the energy barrier separating the two cells.
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The factor 3/2 in Eq. (8) is included so that the potentials of Eqs. (7) and (8) have the same continuum limit as a0 → 0; this is desired for modeling a continuous film. For a honeycomb network however, the duality mapping from Eq. (1) leads to Eq. (8) without the factor of 3/2. The transition temperatures we cite for the Coulomb gas on a triangular grid should therefore be scaled by a factor 2/3 to get the corresponding transitions of a honeycomb network, as opposed to a continuous film.
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