General Method to Determine Replica Symmetry Breaking Transitions

E. Marinari; C. Naitza; F. Zuliani; G. Parisi; M. Picco; F. Ritort

doi:10.1103/PhysRevLett.81.1698

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General Method to Determine Replica Symmetry Breaking Transitions

E. Marinari^*, C. Naitza, and F. Zuliani

G. Parisi^†

M. Picco^‡

F. Ritort^§

Dipartimento di Fisica and INFN, Universita di Cagliari, Via Ospedale 72, 07100 Cagliari, Italy

Dipartimento di Fisica and INFN, Universita di Roma La Sapienza, P. A. Moro 2, 00185 Roma, Italy

LPTHE, Université Pierre et Marie Curie, Paris VI, Université Denis Diderot, Paris VII, Boite 126, Tour 16, 1er étage, 4 place Jussieu, F-75252 Paris CEDEX 05, France

Departament de Fisica Fonamental, Facultat de Fisica, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain

^*Email address: marinari@ca.infn.it
^†Email address: giorgio.parisi@roma1.infn.it
^‡Email address: picco@lpthe.jussieu.fr
^§Email address: ritort@ffn.ub.es

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Phys. Rev. Lett. 81, 1698 – Published 24 August, 1998

DOI: https://doi.org/10.1103/PhysRevLett.81.1698

Abstract

We introduce a new parameter to investigate replica symmetry breaking transitions using finite-size scaling methods. Based on exact equalities initially derived by F. Guerra this parameter is a direct check of the self-averaging character of the spin-glass order parameter. This new parameter can be used to study models with time reversal symmetry but its greatest interest lies in models where this symmetry is absent. We apply the method to long-range and short-range Ising spin-glasses with and without a magnetic field as well as short-range multispin interaction spin-glasses.

Comments & Replies

Marinari et al. Reply:

E. Marinari, C. Naitza, F. Zuliani, G. Parisi, M. Picco, and F. Ritort

Phys. Rev. Lett. 82, 5175 (1999)

Comment on “General Method to Determine Replica Symmetry Breaking Transitions”

Hemant Bokil, A. J. Bray, Barbara Drossel, and M. A. Moore

Phys. Rev. Lett. 82, 5174 (1999)

References (16)

M. Mézard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987); K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801 (1986); K. H. Fischer and J. A. Hertz, Spin Glasses (Cambridge University Press, Cambridge, England, 1991).
A. Blandin, J. Phys. (Paris), Colloq. 39, C6-1499 (1978); A. J. Bray and M. A. Moore, Phys. Rev. Lett. 41, 1068 (1978); G. Parisi, J. Phys. A 13, 1101 (1980); ibid.13, 1887 (1980).
C. M. Newman and D. L. Stein, Phys. Rev. Lett. 76, 515 (1996).
M. Aizenman and P. Contucci, cond-mat 9712129.
F. Guerra, Int. J. Mod. Phys. B 10, 1675 (1996).
D. S. Fisher and D. A. Huse, Phys. Rev. B 38, 386 (1988); 38, 373 (1988).
S. F. Edwards and P. W. Anderson, J. Phys. F 5, 965 (1975).
See the article review by E. Marinari, G. Parisi, and J. J. Ruiz-Lorenzo, in Spin Glasses and Random Fields, A. P. Young (World Scientific, Singapore, 1997).
D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975).
R. Singh and S. Chakravarty, Phys. Rev. Lett. 57, 245 (1986).
D. Badoni, J. C. Ciria, G. Parisi, J. Pech, F. Ritort, and J. J. Ruiz-Lorenzo, Europhys. Lett. 21, 495 (1993).
M. Picco and F. Ritort, J. Phys. I (France) 4, 1619 (1994).
J. R. de Almeida and D. J. Thouless, J. Phys. A 11, 983 (1978).
M. Picco and F. Ritort, cond-mat 9702041.
E. Marinari, G. Parisi, and F. Zuliani, cond-mat 9702253; cond-mat 9802224
A. J. Bray and S. A. Roberts, J. Phys. C 13, 5405 (1980).

[c1] M. Mézard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987); K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801 (1986); K. H. Fischer and J. A. Hertz, Spin Glasses (Cambridge University Press, Cambridge, England, 1991).

[c2] A. Blandin, J. Phys. (Paris), Colloq. 39, C6-1499 (1978); A. J. Bray and M. A. Moore, Phys. Rev. Lett. 41, 1068 (1978); G. Parisi, J. Phys. A 13, 1101 (1980); ibid.13, 1887 (1980).

[c3] C. M. Newman and D. L. Stein, Phys. Rev. Lett. 76, 515 (1996).

[c4] M. Aizenman and P. Contucci, cond-mat 9712129.

[c5] F. Guerra, Int. J. Mod. Phys. B 10, 1675 (1996).

[c6] D. S. Fisher and D. A. Huse, Phys. Rev. B 38, 386 (1988); 38, 373 (1988).

[c7] S. F. Edwards and P. W. Anderson, J. Phys. F 5, 965 (1975).

[c8] See the article review by E. Marinari, G. Parisi, and J. J. Ruiz-Lorenzo, in Spin Glasses and Random Fields, A. P. Young (World Scientific, Singapore, 1997).

[c9] D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975).

[c10] R. Singh and S. Chakravarty, Phys. Rev. Lett. 57, 245 (1986).

[c11] D. Badoni, J. C. Ciria, G. Parisi, J. Pech, F. Ritort, and J. J. Ruiz-Lorenzo, Europhys. Lett. 21, 495 (1993).

[c12] M. Picco and F. Ritort, J. Phys. I (France) 4, 1619 (1994).

[c13] J. R. de Almeida and D. J. Thouless, J. Phys. A 11, 983 (1978).

[c14] M. Picco and F. Ritort, cond-mat 9702041.

[c15] E. Marinari, G. Parisi, and F. Zuliani, cond-mat 9702253; cond-mat 9802224

[c16] A. J. Bray and S. A. Roberts, J. Phys. C 13, 5405 (1980).

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General Method to Determine Replica Symmetry Breaking Transitions

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