Criticality in diluted ferromagnets

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2008, Issue 10, 2008, Pages

  Agliari, Elena ^a   Barra, Adriano ^b,c   Camboni, Federico ^b  

^a UNIVERSITY OF FREIBURG   (Germany)

^b UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^c UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Cavity and replica method; Classical phase transitions (theory); Critical exponents and amplitudes (theory); Gauge theories

Indexed keywords

EID: 56349130706     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2008/10/P10003     Document Type: Article

References (34)

1. Amit D J 1992 Modeling Brain Function: The World of Attractor Neural Network (Cambridge: Cambridge University Press)
2. Agostini A, Barra A and De Sanctis L 2006 Positive-overlap transition and critical exponents in mean field spin glasses J. Stat. Mech. P11015
3. Aizenman M and Contucci P 1998 On the stability of the quenched state in mean field spin glass models J. Stat. Phys. 92 765
4. Albert R and Barabasi A-L 2002 Statistical mechanics of complex networks Rev. Mod. Phys. 74 47
5. Barra A 2006 Irreducible free energy expansion and overlap locking in mean field spin glasses J. Stat. Phys. 123 601
6. Barra A 2008 The mean field Ising model through interpolating techniques J. Stat. Phys. 132 787
7. Barra A 2008 Driven transitions at the onset of ergodicity breaking in gauge invariant complex systems Adv. Complex Syst. submitted
8. Barra A and De Sanctis L 2007 Stability properties and probability distributions of multi-overlaps in diluted spin glasses J. Stat. Mech. P08025
9. Barra A and De Sanctis L 2008 On the mean field spin glass transition Eur. Phys. J. B 64 119
10. Barra A, De Sanctis L and Folli V 2008 Critical behavior of a spin glass on a random graph J. Phys. A: Math. Theor. 41 215005
11. Bianchi A, Contucci P and Giardin C 2003 Thermodynamic limit for mean-field spin models Math. Phys. Electron. J. 9 (6)
12. Bovier A and Gayrard V 1993 The thermodynamics of the Curie-Weiss model with random couplings J. Stat. Phys. 72 643
13. Caldarelli G and Vespignani A 2007 Large Scale Structure and Dynamics of Complex Networks (Singapore: World Scientific)
14. Caldarelli G 2008 Scale Free Networks (Oxford: Oxford Finance)
15. Contucci P and Giardin C 2005 Spin-glass stochastic stability: a rigorous proof Ann. H. Poincaré 6 (5) 915
16. Contucci P and Giardin C 2007 The Ghirlanda-Guerra identities J. Stat. Phys. 126 917
17. Contucci P, Giardin C and Nishimori H 2008 Spin glass identities and the Nishimori line arXiv:0805.0754
18. De Sanctis L and Guerra F 2008 Mean field dilute ferromagnet I. High temperature and zero temperature behavior J. Stat. Phys. 132 759
19. Ellis R S 1985 Large Deviations and Statistical Mechanics (New York: Springer)
20. Erdös P and Renyi A 1959 Publ. Math. 290 6
21. Gallo I and Contucci P 2008 Bipartite mean field spin systems. existence and solution Math. Phys. Electron. J. 14
22. Gerschenfeld A and Montanari A 2007 Reconstruction for models on random graphs Proc. Found. Comput. Sci. 194
23. Ghirlanda S and Guerra F 1998 General properties of overlap distributions in disordered spin systems. Towards Parisi ultrametricity J. Phys. A: Math. Gen. 31 9149
24. Guerra F 1996 About the overlap distribution in mean field spin glass models Int. J. Mod. Phys. B 10 1675
25. Guerra F 2005 An introduction to mean field spin glass theory: methods and results Lecture at Les Houches Winter School
26. Guerra F and Toninelli F L 2003 The infinite volume limit in generalized mean field disordered models Markov Proc. Rel. Fields 9 195
27. Hase M O, de Almeida J R L and Salinas S R 2005 Replica-symmetric solutions of a dilute Ising ferromagnet in a random field Eur. Phys. J. B 47 245
28. Newman M, Watts D and Barabasi A L 2006 The Structure and Dynamics of Networks (Princeton, NJ: Princeton University Press)
29. Newman M E J and Barkema G T 2001 Monte Carlo methods in Statistical Physics (Oxford: Oxford University Press)
30. Parisi G 2000 Stochastic stability Proc. Conf. Disordered and Complex Systems (London)
31. Semerjian G and Weigt M 2004 Approximation schemes for the dynamics of diluted spin models: the Ising ferromagnet on a Bethe lattice J. Phys. A: Math. Gen. 37 5525
32. Skantzos N, Perez Castillo I and Hatchett J 2005 Cavity approach for real variables on diluted graphs and application to synchronization in small-world lattices arXiv:cond-mat/0508609
33. Szalma F and Iglói F 1999 J. Stat. Phys. 95 763
34. Watts D J and Strogatz S H 1998 Collective dynamics of 'small-world' networks Nature 393 409