Hierarchical solutions of the Sherrington-Kirkpatrick model: Exact asymptotic behavior near the critical temperature

Physical Review B - Condensed Matter and Materials Physics

Volumn 74, Issue 5, 2006, Pages

  Janis V ^a   Klic A ^a  

^a INSTITUTE OF PHYSICS   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746923141     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.74.054410     Document Type: Article

References (15)

1. G. Parisi, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/13/3/042 13, 1101 (1980).
2. G. Parisi, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/13/4/009 13, L115 (1980).
3. G. Parisi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.43.1754 43, 1754 (1979).
4. C. De Dominicis and I. Kondor, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.27.606 27, 606 (1983).
5. I. Kondor, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/16/4/006 16, L127 (1980).
6. H. J. Sommers, J. Phys. (France) Lett. JPSLBO 0302-072X 46, L779 (1985).
7. A. Crisanti and T. Rizzo, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.046137 65, 046137 (2002).
8. B. Derrida, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.45.79 45, 79 (1980).
9. E. Gardner, Nucl. Phys. B NUPBBO 0550-3213 240, 747 (1985).
10. D. Elderfield and D. Sherrington, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/16/15/003 16, L497 (1983).
11. V. Janiš, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.214403 71, 214403 (2005).
12. V. Dotsenko, Introduction to the Replica Theory of Disordered Statistical Systems (Cambridge University Press, Cambridge, UK, 2001).
13. T. Aspelmeier and M. Moore, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.177201 90 177201 (2003).
14. K. H. Fischer and J. A. Hertz, Spin Glasses (Cambridge University Press, Cambridge, UK, 1991).
15. Note that a similar result on the instability of the K RSB solution near the critical model was derived within a truncated model by C. De Dominicis and P. Di Francesco, cond-mat/0301066 (unpublished). This calculation was done with only the simplest replica-symmetry-breaking term (∼ ijkl Δ χi Δ χj Δ χk Δ χl and linear in ml, Δ χl for fixed l) in the free energy introduced in Ref.. The asymptotic behavior of this truncated model near the critical temperature is qualitatively correct but the numerical value of the instability (negative value of the spin-glass susceptibility) differs from the exact one in Eq. 31.