Controlling Griffiths' singularities

Abel Klein; J. Fernando Perez

Annales de l'I.H.P. Physique théorique (1996)

  • Volume: 64, Issue: 3, page 309-323
  • ISSN: 0246-0211

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Klein, Abel, and Perez, J. Fernando. "Controlling Griffiths' singularities." Annales de l'I.H.P. Physique théorique 64.3 (1996): 309-323. <http://eudml.org/doc/76716>.

@article{Klein1996,
author = {Klein, Abel, Perez, J. Fernando},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {quenched correlation functions; random field Ising model},
language = {eng},
number = {3},
pages = {309-323},
publisher = {Gauthier-Villars},
title = {Controlling Griffiths' singularities},
url = {http://eudml.org/doc/76716},
volume = {64},
year = {1996},
}

TY - JOUR
AU - Klein, Abel
AU - Perez, J. Fernando
TI - Controlling Griffiths' singularities
JO - Annales de l'I.H.P. Physique théorique
PY - 1996
PB - Gauthier-Villars
VL - 64
IS - 3
SP - 309
EP - 323
LA - eng
KW - quenched correlation functions; random field Ising model
UR - http://eudml.org/doc/76716
ER -

References

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  1. [1] L. Bassalygo and R. Dobrushin, Uniqueness of a Gibbs field with random potential - an elementary approach, Theory Probab. Appl., Vol. 31, 1986, pp. 572-589. Zbl0635.60107MR881577
  2. [2] A. Berretti, Some properties of random Ising models, J. Stat. Phys., Vol. 38, 1985, pp. 483-496. Zbl0624.60116MR788429
  3. [3] H. von Dreifus, A. Klein and J.F. Perez, Taming Griffiths' singularities: infinite differentiability of quenched correlation functions, Commun. Math. Phys., Vol. 170, 1995, pp. 21-39. Zbl0820.60086MR1331689
  4. [4] J. Fröhlich, Mathematical aspects of the Physics of disordered systems, in: "Critical Phenomena Random Systems, Gauge Theories", K. Osterwalder and R. Stora (eds.), Elsevier, 1986. Zbl0669.60098MR880538
  5. [5] J. Fröhlich and J. Imbrie, Improved perturbation expansion for disordered systems: beating Griffiths singularities, Commun. Math. Phys., Vol. 96, 1984, pp. 145-180. Zbl0574.60098MR768253
  6. [6] J. Fröhlich and B. Zegarlinski, The high temperature phase of long range spin glasses, Commun. Math. Phys., Vol. 110, 1987, pp. 121-155. MR885574
  7. [7] G. Gielis and C. Maes, The uniqueness regime of Gibbs field with unbounded disorder, J. Stat. Phys., Vol. 81, 1995, pp. 829-835. Zbl1081.82519MR1359208
  8. [8] R.B. Griffiths, Non-analytic behavior above the critical point in a random Ising ferromagnet, Phys. Rev. Lett., Vol. 23, 1969, pp. 17-19. 
  9. [9] H. Kesten, Percolation Theory for Mathematicians, Birkhauser, 1982. Zbl0522.60097MR692943
  10. [10] H. Kesten, Aspects of first passage percolation, in: "École d'Été de Probabilités de Saint-Flour XIV", P. L. Hennequin, ed., Lecture Notes in Mathematics, Springer, Berlin, Vol. 1180, 1986, pp. 125-264. Zbl0602.60098MR876084
  11. [11] A. Klein, Who is afraid of Griffiths' singularities?, in: "On Three Levels. Micro, Meso and Macroscopic Approaches in Physics", M. Fannes, C. Maes, and A. Verbeure, eds., Plenum Press, New York, 1994, pp. 253-258. Zbl0872.60087
  12. [12] E. Olivieri, J.F. Perez and S.G. Rosa Jr., Some rigorous results on the phase diagram of dilute Ising systems, Phys. Lett., Vol. 94A, 1983, p. 309. 
  13. [13] J.F. Perez, Controlling the effect of Griffiths' singularities in random ferromagnets, Braz. J. Phys., Vol. 23, 1993, pp. 356-362. 
  14. [14] A. Süto, Weak singularity and absence of metastability in random Ising ferromagnets, J. Phys., Vol. A15, 1982, pp. L749-L752. MR682328
  15. [15] G.S. Sylvester, Representations and inequalities for Ising model Ursell functions, Commun. Math. Phys., Vol. 42, 1975, pp. 209-220. MR406301
  16. [16] B. Zegarlinski, Spin glasses and long range interactions at high temperature, J. Stat. Phys., Vol. 47, 1987, pp. 911-930. MR912509

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