No Access

AGING IN A ONE-DIMENSIONAL EDWARDS–ANDERSON SPIN GLASS MODEL WITH LONG-RANGE INTERACTIONS

MARCELO A. MONTEMURRO

Universidad Nacional de Córdoba, FaMAF, Córdoba, Córdoba 5000, Argentina

Search for more papers by this author

and

FRANCISCO A. TAMARIT

Universidad Nacional de Córdoba, FaMAF, Córdoba, Córdoba 5000, Argentina

Search for more papers by this author

https://doi.org/10.1142/S0129183103004449Cited by:2 (Source: Crossref)

Abstract

In this work we study, by means of numerical simulations, the out-of-equilibrium dynamics of the one-dimensional Edwards–Anderson model with long-range interactions of the form ± Jr^-α. In the limit α → 0 we recover the well known Sherrington–Kirkpatrick mean-field version of the model, which presents a very complex dynamical behavior. At the other extreme, for α → ∞ the model converges to the nearest-neighbor one-dimensional system. We focus our study on the dependence of the dynamics on the history of the sample (aging phenomena) for different values of α. The model is known to have mean-field exponents already for values of α = 2/3. Our results indicate that the crossover to the dynamic mean-field occurs at a value of α < 2/3.

Keywords:

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

K. S. Pitzer, M. C. P. de Lima and D. R. Schreiber, J. Phys. Chem. 89, 1854 (1985), DOI: 10.1021/j100256a006. Web of Science, Google Scholar
T. W. Burkhardt and E. Eisenriegler, Phys. Rev. Lett. 74, 3189 (1995), DOI: 10.1103/PhysRevLett.74.3189. Web of Science, ADS, Google Scholar
B. Bergersen and Z. Rácz, Phys. Rev. Lett. 67, 3097 (1991); H. J. Xu, B. Bergersen, and Z. Rácz, Phys. Rev. E 47, 1520 (1993) . Google Scholar
G. Giacomini and J. L. Lebowitz, Phys. Rev. Lett. 76, 1094 (1996). Web of Science, Google Scholar
K. H. Fisher and J. A. Hertz , Spin Glasses, Cambridge Studies in Magnetism ( Cambridge University Press , Cambridge , 1993 ) . Google Scholar
M. A. Ruderman and C. Kittel, Phys. Rev. 96, 99 (1954); T. Kasuya, Prog. Theor. Phys. 16, 45 (1956); K. Yoshida, Phys. Rev. 106, 893 (1957) . Google Scholar
J. P. Bouchaudet al., Spin Glasses and Random Fields, ed. A. P. Young (World Scientific, Singapore, 1997) p. 161. Link, Google Scholar
S. F. Edwards and P. W. Anderson, J. Phys. F 5, 965 (1975), DOI: 10.1088/0305-4608/5/5/017. ADS, Google Scholar
D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1972 (1975), DOI: 10.1103/PhysRevLett.35.1792. Google Scholar
H. Rieger, Ann. Rev. Comp. Phys. II, 295 (1995). Google Scholar
D. S. Fisher and D. A. Huse, Phys. Rev. B 38, 373 (1988), DOI: 10.1103/PhysRevB.38.373. Web of Science, ADS, Google Scholar
G. Parisi, J. Phys. A 13, L371 (1980). Google Scholar
M. Palassini and A. P. Young, Phys. Rev. Lett. 83, 5126 (1999), DOI: 10.1103/PhysRevLett.83.5126. Web of Science, ADS, Google Scholar
M. Palassini and A. P. Young, Phys. Rev. Lett. 85, 3071 (2000). Web of Science, Google Scholar
E. Marinari and G. Parisi, Phys. Rev. Lett. 85, 3332 (2000), DOI: 10.1103/PhysRevLett.85.3332. Web of Science, ADS, Google Scholar
G. Kotliar, P. W. Anderson and D. L. Stein, Phys. Rev. B 27, 602 (1983), DOI: 10.1103/PhysRevB.27.602. Web of Science, ADS, Google Scholar
K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801 (1986), DOI: 10.1103/RevModPhys.58.801. Web of Science, ADS, Google Scholar
H. Rieger, Phys. Rev. B 53, 6418 (1996). Web of Science, Google Scholar
E. Marinari, G. Parisi and D. Rossetti, Eur. Phys. J. B 2, 495 (1998), DOI: 10.1007/s100510050273. Web of Science, ADS, Google Scholar
D. A. Stariolo, M. A. Montemurro, and F. A. Tamarit , cond-mat/0207105 . Google Scholar
E. Marinari, Phys. Rev. Lett. 82, 5175 (1999), DOI: 10.1103/PhysRevLett.82.5175. Web of Science, ADS, Google Scholar