Thermodynamics and universality for mean field quantum spin glasses

Communications in Mathematical Physics

Volumn 274, Issue 3, 2007, Pages 821-839

  Crawford, Nicholas ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34547531886     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-007-0263-x     Document Type: Article

References (27)

1. Aizenman M. and Nachtergaele B. (1994). Geometric aspects of quantum spin states. Commun. Math. Phys. 164: 17-63
2. Aizenman M., Sims R. and Starr S. (2003). Extended variational principle for the Sherrington-Kirkpatrick spin-glass model. Phys. Rev. B 68: 214403
3. Bhatt R., Huse D. and Guo M. (1996). Quantum Griffiths singularities in the transverse-field Ising spin glass. Phys. Rev. B 54: 3336-3342
4. Billingsley P. (1995). Probability and Measure. New York NY, John Wiley & Sons
5. Burkholder D.L. (1966). Martingale transforms. Ann. Math. Stat. 37: 1494-1504
6. Carmona P. and Hu Y. (2006). Universality in Sherrington Kirkpatrick's spin glass model. Annales de l'Institut Henri Poincaré (B) Probability and Statistics 42(2): 215-222
7. Contucci P., Giardina C. and Pule J. (2004). Thermodynamic Limit for Finite Dimensional Classical and Quantum Disordered Systems. Rev. Math. Phys. 16(5): 629-637
8. Cugliandolo L., Grempel D. and daSilva Santos C. (2001). Imaginary-time replica formalism study of a quantum spherical p-spin-glass model. Phys. Rev. B 64: 014403
9. Dirac P.A.M. (1981). The Principles of Quantum Mechanics. Clarendon Press, London
10. Dorlas, T.C.: Probabilistic derivation of a noncommutative version of Varadhan's theorem. Unpublished, June 2002, "http://www.stp.dias.ie/ ~dorlas/tony_index2.html"
11. Fröhlich J., Israel R., Lieb E. and Simon B. (1978). Phase Transitions and Reflection Positivity. I. General Theory and Long Range Lattice Models. Commun. Math. Phys. 62: 1-34
12. Georges A., Parcollet O. and Sachdev S. (2000). Mean field theory of a quantum Heisenberg spin glass. Phys. Rev. Lett. 85: 840
13. Ginibre J. (1969). Existence of phase transitions for quantum lattice system. Commun. Math. Phys. 14: 205
14. Guerra F. (2003). Broken replica symmetry bounds in the mean field spin glass model. Commun. Math. Phys. 233(1): 1-12
15. Guerra F. and Toninelli F.L. (2002). The thermodynamic limit in mean field spin glass models. Commun. Math. Phys. 230(1): 71-79
16. Guerra F. and Toninelli F.L. (2003). The infinite volume limit in generalized mean field disordered models. Markov Process. Related Fields 9(2): 195-207
17. Mézard, M., Parisi, G., Virasoro, M.A.: Spin glass theory and beyond. World Scientific Lecture Notes in Physics, Vol. 9, Teaneck, NJ:World Scientific Publishing Co., Inc., 1987
18. Newman C.M. and Stein D.L. (2001). Are there incongruent ground states in 2D Edwards-Anderson spin glasses?. Commun. Math Phys. 224: 205-218
19. Newman C.M. and Stein D.L. (2003). Ordering and broken symmetry in short-ranged spin glasses. J. Phys.: Condens. Matter 15: R1319-R1364
20. Newman C.M. and Stein D.L. (2003). Nonrealistic behavior of mean field spin glasses. Phys. Rev. Lett. 91: 197205
21. Panchenko D. (2005). Free energy in the generalized Sherrington- Kirkpatrick mean field model. Rev. Math. Phys. 17(7): 793-857
22. Parisi, G.: Field theory, disorder and simulations. World Scientific Lecture Notes in Physics 49, River Edge, NJ:World Scientific Publishing Co., Inc., 1992
23. Ritort F. (1997). Quantum critical effects in mean-field glassy systems. Phys. Rev. B 55: 14096-14099
24. Sachdev S. and Ye J. (1993). Gapless spin-fluid ground state in a random quantum Heisenberg magnet. Phys. Rev. Lett. 70: 3339
25. De Sanctis L. (2007). Structural Properties of the Disordered Spherical and Other Mean Field Spin Models. J. Stat. Phys. 26: 817-835
26. Talagrand, M.: Spin Glasses: A Challenge for Mathematicians. Cavity and Mean Field Models. A Series of Modern Surveys in Mathematics, Vol 46. Berlin:Springer-Verlag, 2003
27. Talagrand M. (2006). The Parisi formula. Ann. of Math. (2) 163(1): 221-263