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Large deviations for Ising spin glasses with constrained disorder

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Abstract

We consider ad-dimensional Ising spin glass and construct lower bounds for the mean free energy density which, in general, improve the classical lower bounds given by the annealed free energy density. The bounds are achieved by introducing generalized finite-volume free energy densities. The large-deviations aspects of the problem are displayed and examples discussed.

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References

  1. F. Comets, Large deviation estimates for a conditional probability distribution. Application to random interaction Gibbs measures,Prob. Theory Related Fields 80:407 (1987).

    Google Scholar 

  2. R. S. Ellis,Entropy, Large Deviations and Statistical Mechanics (Springer-Verlag, Berlin, 1985).

    Google Scholar 

  3. F. Ledrappier, Pressure and variational principles for random Ising models,Commun. Math. Phys. 56:297 (1977).

    Google Scholar 

  4. F. Koukiou, Rigorous bonds for the free energy of the short range Ising spin glass model,Europhys. Lett. 7:297 (1992).

    Google Scholar 

  5. M. Mezard, G. Parisi, and M. Virasoro,Spin Glass Theory and Beyond (World Scientific, Singapore, 1988).

    Google Scholar 

  6. M. Pasquini, G. Paladin, and M. Serva, Sequence of constrained annealed averages for one-dimensional disordered systems,Phys. Rev. E, submitted.

  7. G. Paladin, M. Pasquini, and M. Serva, Constrained annealing for systems with quenched disorder,J. Mod. Phys. A, to appear.

  8. G. Paladin, M. Pasquini, and M. Serva, Ferrimagnetism in a disordered Ising model,J. Phys. I France 4:1597 (1994).

    Google Scholar 

  9. G. Toulose and J. Vannimenus, On the connection between spin glasses and gauge field theories,Phys. Rep. 67:47 (1980).

    Google Scholar 

  10. M. F. Thorpe and D. Beeman, Thermodynamics of an Ising model with random exchange interactions,Phys. Rev. B 14:188 (1976).

    Google Scholar 

  11. J. Deutsch and G. Paladin, The product of random matrices in a microcanonical ensemble,Phys. Rev. Lett. 62:695 (1988).

    Google Scholar 

  12. D. Ruelle,Statistical Mechanics (Benjamin, New York, 1969).

    Google Scholar 

  13. M. Serva and G. Paladin, Gibbs thermodynamical potentials for disordered systems,Phys. Rev. Lett. 70: 105 (1993).

    Google Scholar 

  14. J. L. Van Hemmen and R. G. Palmer, The thermodynamic limit and the replica method for short range random systems,J. Phys. A: Math. Gen. 15:3881 (1982).

    Google Scholar 

  15. J. L. Van Hemmen, A. C. D. Van Enter, and J. Conisins On a spin glass model,Z. Phys. B Condensed Matter 50:311 (1993).

    Google Scholar 

  16. P. A. Vuillermot, Thermodynamics of quenched random spin systems and application to the problem of phase transition in magnetic (spin) glasses,J. Phys. A: Math. Gen.,10:1319 (1987).

    Google Scholar 

  17. G. Paladin and A. Vulpiani, Anomalous scaling laws in multifractal objectsPhys. Rep. 156:141 (1987).

    Google Scholar 

  18. L. Saul and M. Kardar, Exact integer algorithm for the two-dimensional Ising spin glass,Phys. Rev. E 48:48 (1993).

    Google Scholar 

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Scarlatti, S., Serva, M. & Pasquini, M. Large deviations for Ising spin glasses with constrained disorder. J Stat Phys 80, 337–356 (1995). https://doi.org/10.1007/BF02178362

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