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Equilibrium phase transitions in Josephson junction arrays

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Complex Behaviour of Glassy Systems

Part of the book series: Lecture Notes in Physics ((LNP,volume 492))

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Abstract

I review several problems dealing with the equilibrium behavior of classical two dimensional Josephson junction arrays in applied magnetic fields. Specific attention is given to the cases of a uniform field with average flux density per unit cell of f=0, f=1/2, f=1/q and f=1/2−1/q. Several models incorporating the effects of randomness on the Josephson array are also reviewed. These include the case of a random vortex pinning potential and its effects on vortex lattice order, and the spin glass, gauge glass, and positionally disordered array.

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References

  • Bagchi K., Anderson H. C., Swope W. (1996): Computer simulation study of the melting transition in two dimensions. Phys. Rev. Lett. 76, 255

    Article  ADS  Google Scholar 

  • Benz S. P., Forrester M. G., Tinkham M., Lobb C. J. (1988): Positional disorder in superconducting wire networks and Josephson junction arrays. Phys. Rev. B 38, 2869

    Article  ADS  Google Scholar 

  • Bokil H. S., Young A. P. (1996): Study of chirality in the two-dimensional XY spin glass. Preprint, cond-mat/9512042

    Google Scholar 

  • Caillol J. M., Levesque D., Weis J. J., Hansen J. P. (1982): A Monte Carlo study of the classical two-dimensional one-component plasma. J. Stat. Phys. 28, 325

    Article  ADS  Google Scholar 

  • Caillol J. M., Levesque D. (1986): Low-density phase diagram of the two-dimensional Coulomb gas. Phys. Rev. B 33, 499

    Article  ADS  Google Scholar 

  • Chakrabarti A., Dasgupta C. (1988): Phase transition in positionally disordered Josephson-junction arrays in a transverse magnetic field. Phys. Rev. B 37, 7557

    Article  ADS  Google Scholar 

  • Choi M. Y., Chung J. S., Stroud D. (1987): Positional disorder in a Josephsonjunction array. Phys. Rev. B 35 1669

    Article  ADS  Google Scholar 

  • Choquard Ph., Clerouin J. (1983): Cooperative phenomena below melting of the one-component two-dimensional plasma. Phys. Rev. Lett. 50, 2086

    Article  ADS  Google Scholar 

  • Chudnovsky E. M. (1991): Orientational and positional order in flux lattices of type-II superconductors. Phys. Rev. B 43, 7831

    Article  ADS  Google Scholar 

  • Cieplak M., Banavar J. R., Li M. S., Khurana A. (1992): Frustration, scaling, and local gauge invariance. Phys. Rev. B 45, 786

    Article  ADS  Google Scholar 

  • Cohn M. B., Rzchoswki M. S., Benz S. P., Lobb C. J. (1991): Vortex-defect interactions in Josephson-junction arrays. Phys. Rev. B 43, 12823

    Article  ADS  Google Scholar 

  • Dodgson M. J. W. (1995): Investigation on the ground states of a model thin film superconductor on a sphere. Preprint, cond-mat/9512124

    Google Scholar 

  • Fisher D. S. (1980): Flux-lattice melting in a thin-film superconductor. Phys. Rev. B 22, 1190

    Article  ADS  Google Scholar 

  • Fisher M. P. A., Tokuyasu T. A., Young A. P. (1991): Vortex variable-rangehopping resistivity in superconducting films. Phys. Rev. Lett. 66, 2931

    Article  ADS  Google Scholar 

  • Forrester M. B., Lee H. J., Tinkham M., Lobb C. J. (1988): Positional disorder in Josephson-junction arrays: Experiments and simulations. Phys. Rev. B 37, 5966

    Article  ADS  Google Scholar 

  • Forrester M. G., Benz S. P., Lobb C. J. (1990): Monte Carlo simulations of Josephson-junction arrays with positional disorder. Phys. Rev. B 41, 8749

    Article  ADS  Google Scholar 

  • Fradkin E., Huberman B. A., Shenker S. H. (1978): Gauge symmetries in random magnetic systems. Phys. Rev. B 18, 4789

    Article  ADS  Google Scholar 

  • Franz M., Teitel S. (1995): Vortex-lattice melting in two-dimensional superconducting networks and films. Phys. Rev. B 51 6551

    Article  ADS  Google Scholar 

  • Franz M., Teitel S. (1996): Effect of random pinning on 2D vortex lattice correlations. In preparation

    Google Scholar 

  • Friesen M. (1995): Critical and non-critical behavior of the Kosterlitz-Thouless-Berezinskii transition. Phys. Rev. B 53, R514

    Google Scholar 

  • Giamarchi T., Le Doussal P. (1994): Elastic theory of pinned flux lattices. Phys. Rev. Lett. 72, 1530

    Article  ADS  Google Scholar 

  • Gingras M. J. P. (1992): Numerical study of vortex-glass order in randomsuperconductor and related spin-glass models. Phys. Rev. B 45, 7547

    Article  ADS  MATH  Google Scholar 

  • Giovannella C., Tinkham M., eds. (1995): Macroscopic Quantum Phenomena and Coherence in Superconducting Networks. (World Scientific, Singapore)

    Google Scholar 

  • Granato E., Kosterlitz J. M. (1986): Quenched disorder in Josephson-junction arrays in a transverse magnetic field. Phys. Rev. B 33, 6533

    Article  ADS  Google Scholar 

  • Granato E., Nightingale M. P. (1993): Chiral exponents of the square-lattice frustrated XY model: a Monte Carlo transfer-matrix calculation. Phys. Rev. B 48, 7438

    Article  ADS  Google Scholar 

  • Grest G. S. (1989): Critical behavior of the two-dimensional uniformly frustrated charged Coulomb gas. Phys. Rev. B 39, 9267

    Article  ADS  Google Scholar 

  • Gupta P., Teitel S. (1996): Phase diagram of the 2D dense lattice Coulomb gas. In preparation

    Google Scholar 

  • Halsey T. C. (1985): Josephson-junction array in an irrational magnetic field: A superconducting glass? Phys. Rev. Lett. 55, 1018

    Article  ADS  Google Scholar 

  • Halsey T. C. (1988): On the critical current of a Josephson junction array in a magnetic field. Physica B 152, 22

    Article  ADS  Google Scholar 

  • Hattel S. A., Wheatley J. M. (1994): Depinning phase transitions in two-dimensional lattice Coulomb solids. Phys. Rev. B 50 16590

    Article  ADS  Google Scholar 

  • Hattel S. A., Wheatley J. M. (1995): Flux lattice melting and depinning in the weakly frustrated two-dimensional XY model. Phys. Rev. B 51, 11951

    Article  ADS  Google Scholar 

  • Hu J., MacDonald A. H. (1993): Two-dimensional vortex lattice melting. Phys. Rev. Lett. 71, 432

    Article  ADS  Google Scholar 

  • José J. V., Kadanoff L. P., Kirkpatrick S., Nelson D. R. (1977): Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model. Phys. Rev. B 16, 1217

    Article  ADS  Google Scholar 

  • Kato Y., Nagaosa N. (1993): Monte Carlo simulation of two-dimensional flux-linelattice melting. Phys. Rev. B 48, 7383

    Article  ADS  Google Scholar 

  • Kawamura H., Tanemura M. (1987): Chiral order in a two-dimensional XY spin glass. Phys. Rev. B 36, 7177

    Article  ADS  Google Scholar 

  • Knops Y. M. M., Nienhuis B., Knops H. J. F., Blöte J. W. J. (1994): 19-vertex version of the fully frustrated XY model. Phys. Rev. B 50, 1061

    Article  ADS  Google Scholar 

  • Kolahchi M. R., Straley, J. P. (1991): Ground state of the uniformly frustrated two-dimensional XY model near f=1/2. Phys. Rev. B 43, 7651

    Article  ADS  Google Scholar 

  • Korshunov S. E. (1986): Phase transitions in two-dimensional uniformly frustrated XY models. II. General scheme. J. Stat. Phys. 43, 17

    Article  MathSciNet  ADS  Google Scholar 

  • Korshunov S. E. (1993): Replica symmetry breaking in vortex glasses. Phys. Rev. B 48, 3669

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Larkin A. I., Ovchinnikov Yu. N. (1979) Pinning in type II superconductors. J. Low Temp. Phys. 34, 409

    Article  ADS  Google Scholar 

  • Lee D. H., Joannopoulos J. D., Negele J. W., Landau D. P. (1986): Symmetry analysis and Monte Carlo study of a frustrated antiferromagnetic planar (XY) model in two dimensions. Phys. Rev. B 33, 450

    Article  ADS  Google Scholar 

  • Lee J., Kosterlitz J. M., Granato E. (1991): Monte Carlo study of frustrated XY models on a triangular and square lattice. Phys. Rev. B 43, 11531

    Article  ADS  Google Scholar 

  • Lee J.-R. (1994): Phase transitions in the two-dimensional classical lattice Coulomb gas of half-integer charges. Phys. Rev. B 49, 3317

    Article  ADS  Google Scholar 

  • Lee J.-R., Teitel S. (1992): Phase transitions in classical two-dimensional lattice Coulomb gases. Phys. Rev. B 46, 3247

    Article  ADS  Google Scholar 

  • Lee S., Lee K.-C. (1994): Phase transitions in the fully frustrated XY model studied by the microcanonical Monte Carlo technique. Phys. Rev. B 49, 15184

    Article  ADS  Google Scholar 

  • Lee S., Lee K.-C. (1995): Phase transitions in the uniformly frustrated XY model with frustration parameter f=1/3 studied with use of the microcanonical Monte Carlo technique. Phys. Rev. B 52, 6706

    Article  ADS  Google Scholar 

  • Levin Y., Li X., Fisher M. E. (1994): Coulombic criticality in general dimensions. Phys. Rev. Lett. 73, 2716

    Article  ADS  Google Scholar 

  • Li Y.-H., Teitel S. (1990): Flux flow resistance in frustrated Josephson junction arrays. Phys. Rev. Lett. 65, 2595

    Article  ADS  Google Scholar 

  • Li Y.-H., Teitel S. (1991): The effect of random pinning sites on behavior in Josephson junction arrays. Phys. Rev. Lett. 67, 2894

    Article  ADS  Google Scholar 

  • Lidmar J., Wallin M. (1996): Monte Carlo simulation of a two-dimensional continuum Coulomb gas. Preprint, cond-mat/9607025

    Google Scholar 

  • Lobb C. J., Abraham D. W., Tinkham M. (1983): Theoretical interpretation of resistive transition data from arrays of superconducting weak links. Phys. Rev. B 27, 150 (1983)

    Article  ADS  Google Scholar 

  • Minnhagen P. (1987): The two-dimensional Coulomb gas, vortex unbinding, and superfluid-superconducting films. Rev. Mod. Phys. 59, 1001

    Article  ADS  Google Scholar 

  • Minnhagen P., Wallin M. (1987): New phase diagram for the two-dimensional Coulomb gas. Phys. Rev. B 36, 5620

    Article  ADS  Google Scholar 

  • Minnhagen P., Wallin M. (1989): Results for the phase diagram of the two-dimensional Coulomb gas. Phys. Rev. B 40, 5109

    Article  ADS  Google Scholar 

  • Miyshita S., and Shiba H. (1984): Nature of the phase transition of the two-dimensional antiferromagnetic plane rotor model on the triangular lattice. J. Phys. Soc. Jpn. 53, 1145

    Article  ADS  Google Scholar 

  • Nattermann T., Scheidl S., Korshunov S. E., Li M. S. (1995): Absence of reentrance in the two-dimensional XY-model with random phase shifts. J. Phys. I France 5, 565

    Article  Google Scholar 

  • Nelson D. R., Halperin B. I. (1979): Dislocation-mediated melting in two dimensions. Phys. Rev. B 19, 2457

    Article  ADS  Google Scholar 

  • Nicolaides D. B. (1991): Monte Carlo simulation of the fully frustrated XY model. J. Phys. A 24, L231

    Google Scholar 

  • Nightingale M. P., Granato E., Kosterlitz J. M. (1995): Conformal anomaly and critical exponents of the XY Ising model. Phys. Rev. B 52, 7402

    Article  ADS  Google Scholar 

  • Ohta T., Jasnow D. (1979): XY model and the superfluid density in two dimensions. Phys. Rev. B 20, 139

    Article  ADS  Google Scholar 

  • Olsson P. (1995a): Monte Carlo analysis of the two-dimensional XY model. II. Comparison with the Kosterlitz renormalization group equations. Phys. Rev. B 52, 4511

    Article  ADS  Google Scholar 

  • Olsson P. (1995b): Two phase transitions in the fully frustrated XY model. Phys. Rev. Lett. 75, 2758

    Article  ADS  Google Scholar 

  • Ozeki Y., Nishimori H. (1993): Phase diagram of gauge glasses. J. Phys. A 26, 3399

    Article  ADS  MathSciNet  Google Scholar 

  • Ramirez-Santiago G., José J. V. (1994): Critical exponents of the fully frustrated two-dimensional XY model. Phys. Rev. B 49, 9567

    Article  ADS  Google Scholar 

  • Ray P., Moore M. A. (1992): Chirality-glass and spin-glass correlations in the two-dimensional random-bond XY model. Phys. Rev. B 45, 5361

    Article  ADS  Google Scholar 

  • Rubinstein M., Shraiman B., Nelson D. R. (1983): Two-dimensional XY magnets with random Dzyaloshinskii-Moriya interactions. Phys. Rev. B 27, 1800

    Article  ADS  MathSciNet  Google Scholar 

  • Rzchowski M. S., Benz S. P., Tinkham M., Lobb C. J. (1990): Vortex pinning in Josephson-junction arrays. Phys. Rev. B 42, 2041

    Article  ADS  Google Scholar 

  • Šášik R., Stroud D. (1994): Calculation of the shear modulus of a two-dimensional vortex lattice. Phys. Rev. B 49, 16074

    Article  ADS  Google Scholar 

  • Scheidl S. (1996): Glassy vortex state in a two-dimensional XY-model. Preprint, cond-mat/9601131

    Google Scholar 

  • Straley J. P. (1988): Magnetic field effects in Josephson networks. Phys. Rev. B 38, 11225

    Article  ADS  Google Scholar 

  • Straley J. P., Barnett G. M. (1993): Phase diagram for a Josephson network in a magnetic field. Phys. Rev. B 48, 3309

    Article  ADS  Google Scholar 

  • Standburg K. J. (1988): Two-dimensional melting. Rev. Mod. Phys. 60, 69

    Article  Google Scholar 

  • Tang L.-H. (1996): Vortex statistics in a disordered two-dimensional XY model. Preprint, cond-mat/9602162

    Google Scholar 

  • Teitel S., Jayaprakash C. (1983a): Phase transitions in frustrated two dimensional XY models. Phys. Rev. B 27, 598

    Article  ADS  Google Scholar 

  • Teitel S., Jayaprakash C. (1983b): Josephson junction arrays in transverse magnetic fields. Phys. Rev. Lett. 51, 1999

    Article  ADS  Google Scholar 

  • Tešanović Z., Xing L. (1991): Critical fluctuations in strongly type-II quasi-two-dimensional superconductors. Phys. Rev. Lett. 67, 2729

    Article  ADS  Google Scholar 

  • Théron R., Korshunov S. E., Simond J. B., Leemann Ch., Martinoli P. (1994): Observation of domain-wall superlattice states in a frustrated triangular array of Josephson junctions. Phys. Rev. Lett. 72, 562

    Article  ADS  Google Scholar 

  • Thijssen J. M., Knops H. J. F. (1988a): Monte Carlo study of the Coulomb-gas representation of frustrated XY models. Phys. Rev. B 37, 7738

    Article  ADS  Google Scholar 

  • Thijssen J. M., Knops H. J. F. (1988b): Analysis of a new set of renormalization equations for the Kosterlitz-Thouless transition. Phys. Rev. B 38, 9080

    Article  ADS  Google Scholar 

  • Thijssen J. M., Knops H. J. F. (1990): Monte Carlo transfer-matrix study of the frustrated XY model. Phys. Rev. B 42, 2438

    Article  ADS  Google Scholar 

  • Vallat A., Beck H. (1992): Classical frustrated XY model: Continuity of the groundstate energy as a function of the frustration. Phys. Rev. Lett. 68, 3096

    Article  ADS  Google Scholar 

  • Vallat A., Beck H. (1994): Coulomb-gas representation of the two-dimensional XY model on a torus. Phys. Rev. B 50, 4015

    Article  ADS  Google Scholar 

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

    Google Scholar 

  • Young A. P. (1979): Melting of the vector Coulomb gas in two dimensions. Phys. Rev. B 19, 1855

    Article  ADS  Google Scholar 

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Miguel Rubí Conrado Pérez-Vicente

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© 1997 Springer-Verlag

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Teitel, S. (1997). Equilibrium phase transitions in Josephson junction arrays. In: Rubí, M., Pérez-Vicente, C. (eds) Complex Behaviour of Glassy Systems. Lecture Notes in Physics, vol 492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104839

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  • DOI: https://doi.org/10.1007/BFb0104839

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