The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  • Aizenman, Michael; Sims, Robert; Starr, Shannon L. Mean-field spin glass models from the cavity-ROSt perspective. Prospects in mathematical physics, 1--30, Contemp. Math., 437, Amer. Math. Soc., Providence, RI, 2007. MR2354653
  • Spin glasses. Edited by Erwin Bolthausen and Anton Bovier. Lecture Notes in Mathematics, 1900. Springer, Berlin, 2007. x+179 pp. ISBN: 978-3-540-40902-1; 3-540-40902-5 MR2309595
  • Spin glasses: statics and dynamics. Papers from the International Summer School held in Paris, June 25–July 6, 2007. Edited by Anne Boutet de Monvel and Anton Bovier. Progress in Probability, 62. Birkhäuser Verlag, Basel, 2009. xii+278 pp. ISBN: 978-3-7643-8999-4 MR2761195
  • Bovier, Anton. Statistical mechanics of disordered systems. A mathematical perspective. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, 2006. xiv+312 pp. ISBN: 978-0-521-84991-3; 0-521-84991-8 MR2252929
  • Bovier, Anton; Klimovsky, Anton. The Aizenman-Sims-Starr and Guerra's schemes for the SK model with multidimensional spins. Electron. J. Probab. 14 (2009), no. 8, 161--241. MR2471664
  • Andrea Crisanti and Hans-Jürgen Sommers. The spherical p-spin interaction spin glass model: the statics. Zeitschrift für Physik B Condensed Matter, 87(3):341--354, 1992.
  • Fyodorov, Yan V.; Bouchaud, Jean-Philippe. Statistical mechanics of a single particle in a multiscale random potential: Parisi landscapes in finite-dimensional Euclidean spaces. J. Phys. A 41 (2008), no. 32, 324009, 25 pp. MR2425780
  • Fyodorov, Yan V.; Sommers, H.-J. Classical particle in a box with random potential: exploiting rotational symmetry of replicated Hamiltonian. Nuclear Phys. B 764 (2007), no. 3, 128--167. MR2293452
  • Guerra, Francesco. Broken replica symmetry bounds in the mean field spin glass model. Comm. Math. Phys. 233 (2003), no. 1, 1--12. MR1957729
  • Francesco Guerra and Fabio~Lucio Toninelli. The infinite volume limit in generalized mean field disordered models. Markov Process. Related Fields, 9(2):195--207, 2003.
  • Mézard, Marc; Parisi, Giorgio; Virasoro, Miguel Angel. Spin glass theory and beyond. World Scientific Lecture Notes in Physics, 9. World Scientific Publishing Co., Inc., Teaneck, NJ, 1987. xiv+461 pp. ISBN: 9971-50-115-5; 9971-50-116-3 MR1026102
  • Panchenko, Dmitry. A question about the Parisi functional. Electron. Comm. Probab. 10 (2005), 155--166 (electronic). MR2162815
  • Panchenko, Dmitry. Free energy in the generalized Sherrington-Kirkpatrick mean field model. Rev. Math. Phys. 17 (2005), no. 7, 793--857. MR2159369
  • Talagrand, Michel. Spin glasses: a challenge for mathematicians. Cavity and mean field models. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], 46. Springer-Verlag, Berlin, 2003. x+586 pp. ISBN: 3-540-00356-8 MR1993891
  • Talagrand, Michel. Free energy of the spherical mean field model. Probab. Theory Related Fields 134 (2006), no. 3, 339--382. MR2226885
  • Talagrand, Michel. The Parisi formula. Ann. of Math. (2) 163 (2006), no. 1, 221--263. MR2195134
  • Talagrand, Michel. Mean field models for spin glasses. Volume I. Basic examples. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], 54. Springer-Verlag, Berlin, 2011. xviii+485 pp. ISBN: 978-3-642-15201-6 MR2731561
  • Talagrand, Michel. Mean field models for spin glasses. Volume I. Basic examples. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], 54. Springer-Verlag, Berlin, 2011. xviii+485 pp. ISBN: 978-3-642-15201-6 MR2731561
  • Akiva~M. Yaglom. Some classes of random fields in n-dimensional space, related to stationary random processes. Theor. Probab. Applic., 2(3):273--320, 1957.
  • Yaglom, A. M. Correlation theory of stationary and related random functions. Vol. I. Basic results. Springer Series in Statistics. Springer-Verlag, New York, 1987. xiv+526 pp. ISBN: 0-387-96268-9 MR0893393
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.