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Energy Landscape of m-Component Spin Glasses

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Abstract

Although it is established that typical spin glasses [Méz87] order at a critical temperature \(T_\mathrm{{SG}}\) for \(d\ge 3\) [Bal00, Kaw01, Lee03], the nature of the low-temperature phase of spin glasses under the upper critical dimension \(d_u=6\) is still a matter of debate (Sect. 1.1.2 ) .

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Notes

  1. 1.

    For example, in [Bey12] the infinite-m limit is used to derive exact relations in the one-dimensional spin glass with power law interactions.

  2. 2.

    By quench we mean the minimization of the energy throughout the best possible satisfaction of the local constraints, i.e. a quench is a dynamical procedure, as explained in Appendix F.1.1. Be careful not to confuse it with other uses of the same term. For example, those quenches have little to do with the quenched approximation used in QCD, or the quenched disorder, that is a property of the system.

  3. 3.

    In addition to [Ber04c, BJ11] cited several times in this chapter, one can e.g. see [Bla14] for systems without quenched disorder, and [Bur07] for spin glasses.

  4. 4.

    To our knowledge, the only reference where a non-trivial behavior of the self-overlap was found is in [BJ11]. Yet, in this case it was in the study of ISs from finite temperature, and in the chiral sector (they worked with \(m=3\)).

  5. 5.

    The point correlation length \(\xi _2^\mathrm {point}\) behaves analogously.

  6. 6.

    Note that the definition of the coherence length in [Ber04c] is different from ours.

References

  1. R. Alvarez Baños, A. Cruz, L.A. Fernandez, J.M. Gil-Narvion, A. Gordillo-Guerrero, M. Guidetti, A. Maiorano, F. Mantovani, E. Marinari, V. Martin-Mayor, J. Monforte-Garcia, A. Muñoz Sudupe, D. Navarro, G. Parisi, S. Perez-Gaviro, J.J. Ruiz-Lorenzo, S.F. Schifano, B. Seoane, A. Tarancon, R. Tripiccione, D. Yllanes (Janus Collaboration), J. Stat. Mech. 2010, P06026 (2010). doi:10.1088/1742-5468/2010/06/P06026. arXiv:1003.2569

    Google Scholar 

  2. T. Aspelmeier, M.A. Moore, Phys. Rev. Lett. 92, 077201 (2004)

    Article  ADS  Google Scholar 

  3. M. Baity-Jesi: Energy landscape in three-dimensional Heisenberg spin glasses. Master’s thesis, Sapienza, Universitá di Roma, Rome, Italy (January 2011). arXiv:1503.08409

  4. M. Baity-Jesi, L.A. Fernandez, V. Martin-Mayor, J.M. Sanz, Phys. Rev. 89, 014202 (2014). doi:10.1103/PhysRevB.89.014202. arXiv:1309.1599

    Article  ADS  Google Scholar 

  5. H.G. Ballesteros, A. Cruz, L.A. Fernandez, V. Martin-Mayor, J. Pech, J.J. Ruiz-Lorenzo, A. Tarancon, P. Tellez, C.L. Ullod, C. Ungil, Phys. Rev. B 62, 14237–14245 (2000). doi:10.1103/PhysRevB.62.14237. arXiv:cond-mat/0006211

    Google Scholar 

  6. F. Belletti, A. Cruz, L.A. Fernandez, A. Gordillo-Guerrero, M. Guidetti, A. Maiorano, F. Mantovani, E. Marinari, V. Martin-Mayor, J. Monforte, A. Muñoz, Sudupe, D. Navarro, G. Parisi, S. Perez-Gaviro, J.J. Ruiz-Lorenzo, S.F. Schifano, D. Sciretti, A. Tarancon, R. Tripiccione, D. Yllanes (Janus Collaboration), J. Stat. Phys. 135, 1121 (2009). doi:10.1007/s10955-009-9727-z. arXiv:0811.2864

    Google Scholar 

  7. L. Berthier, A.P. Young, Phys. Rev. B 69, 184423 (2004)

    Article  ADS  Google Scholar 

  8. F. Beyer, M. Weigel, M. Moore, Phys. Rev. B 86, 014431 (2012)

    Article  ADS  Google Scholar 

  9. T. Blanchard, F. Corberi, L. Cugliandolo, M. Picco, Europhys. Lett. 106, 66001 (2014)

    Article  ADS  Google Scholar 

  10. Z. Burda, A. Krzywicki, O. Martin, Phys. Rev. E 76, 051107 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  11. A. Cavagna, Phys. Rep. 476, 51–124 (2009). arXiv:0903.4264

    Article  ADS  Google Scholar 

  12. P. Contucci, C. Giardinà, C. Giberti, C. Vernia, Phys. Rev. Lett. 96, 217204 (2006). doi:10.1103/PhysRevLett.96.217204

    Article  ADS  Google Scholar 

  13. J. de Almeida, R. Jones, J. Kosterlitz, D. Thouless, J. Phys. C: Solid State Phys. 11, L871 (1978). doi:10.1088/0022-3719/11/21/005. http://stacks.iop.org/0022-3719/11/i=21/a=005

    Google Scholar 

  14. J. Green, A. Bray, M. Moore, J. Phys. A 15, 2307 (1982)

    Article  ADS  Google Scholar 

  15. M.B. Hastings, J. Stat. Phys. 99, 171 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  16. H. Kawamura, M. Li, Phys. Rev. Lett. 87, 18 (2001)

    Google Scholar 

  17. F. Krzakala, O.C. Martin, Phys. Rev. Lett. 85, 3013 (2000). doi:10.1103/PhysRevLett.85.3013

    Article  ADS  Google Scholar 

  18. L.W. Lee, A. Dhar, A.P. Young, Phys. Rev. E 71, 036146 (2005)

    Article  ADS  Google Scholar 

  19. L.W. Lee, A.P. Young, Phys. Rev. Lett. 90, 227203 (2003). doi:10.1103/PhysRevLett.90.227203

    Article  ADS  MathSciNet  Google Scholar 

  20. M. Mézard, G. Parisi, M. Virasoro, Spin-Glass Theory and Beyond (World Scientific, Singapore, 1987)

    MATH  Google Scholar 

  21. M.A. Moore, Phys. Rev. E 86, 031114 (2012)

    Article  ADS  Google Scholar 

  22. L. Viana, J. Phys. A 21, 803 (1988)

    Article  ADS  MathSciNet  Google Scholar 

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  1. Institut de Physique Théorique, DRF, CEA Saclay, Gif-sur-Yvette, France

    Marco Baity Jesi

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  1. Marco Baity Jesi
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Correspondence to Marco Baity Jesi .

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Baity Jesi, M. (2016). Energy Landscape of m-Component Spin Glasses. In: Spin Glasses. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-41231-3_4

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