Diffusive scaling of the spectral gap for the dilute Ising lattice-gas dynamics below the percolation threshold

Probability Theory and Related Fields

Volumn 120, Issue 4, 2001, Pages 497-534

  Cancrini, N ^a   Martinelli, F ^b  

^a UNIVERSITY OF L'AQUILA   (Italy)

^b ROMA TRE UNIVERSITY   (Italy)

Author keywords

Equivalence of ensembles; Kawasaki dynamics; Random ferromagnet; Spectral gap

Indexed keywords

EID: 0035612841     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00008790     Document Type: Article

References (23)

1. Alexander, K.S., Cesi, F., Chayes, L., Maes, C., Martinelli, F.: Convergence to Equilibrium of Random Ising Models in the Griffiths' phase. J. Stat. Phys., 92, 337-351 (1998)
2. Aizenman, M., Chayes, J.T., Chayes, L., Newman, C.M.: Tha phase boundary in dilute and random Ising and Potts ferromagnets. J. Phys. A: Math. Gen., 20, L313-1318 (1987)
3. Bassalygo, L.A., Dobrushin, R.L.: Uniqueness of a Gibbs field with random potential - an elementary approach, Theory Prob. Appl., 31(4), 572 (1986)
4. Bertini, L., Zegarlinski, B.: Coercive inequalities for Kawasaki dynamics. The product case, Markov Processes and Rel. Fields, 5, 125-162 (1999)
5. Cancrini, N., Cesi, F., Martinelli, F.: Kawasaki dynamics at low temperature, J. Stat. Phy., 95, 219-275 (1999)
6. Cancrini, N., Martinelli, F.: Comparison of finite volume canonical and grand canonical Gibbs measures under a mixing condition, Markov Proc. Rel. Fields, 6, 1-49 (2000)
7. Cancrini, N., Martinelli, F.: On the spectral gap of Kawasaki dynamics under a mixing condition revisited. J. Math. Phys., 41(3) (2000)
8. Cesi, F., Maes, C., Martinelli, F.: Relaxation of Disordered magnets in the Griffiths regime. Comm. Math. Phys., 188, 135 (1997)
9. Cesi, F., Maes, C., Martinelli, F: Relaxation to equilibrium for two dimensional disordered Ising systems in the Griffiths phase. Comm. Math. Phys., 189, 323 (1997)
10. Von Dreyfus, H., Klein, A., Perez, J.F.: Taming Griffiths singularities: infinite differentiability of quenched correlations functions. Comm. Math. Phys., 170. 21 (1995)
11. Fröhlich, J.: Mathematical aspects of the physics of disordered systems in "Critical Phenomena, Random Systems, Gauge Theories" Eds. K. Osterwalder and R. Stora, Elsevier (1986)
12. Georgii, H.O.: Spontaneous magnetization of randomly dilute ferromagnets. J. Stat. Phy., 25, 369 (1981)
13. Gielis, G., Maes, C.: Local analyticity and bounds on the truncated correlation functions in disordered systems. Markov Proc. Relat. Fields, 1, 459 (1995)
14. Gielis, G., Maes, C.: The uniqueness regime of Gibbs fields with unbounded disorder. J. Stat. Phys., 81(3/4), 829 (1995)
15. Griffiths, R.: Non-analytic behaviour above the critical point in a random Ising ferromagnet. Phys. Rev. Lett., 23, 17 (1969)
16. Grimmett, G.: Percolation (Grundheren Der Mathematischen Wissenschaften, 321) Springer Verlag (1999)
17. Häggström, O., Schonmann, R.H., Steif, J.A.: The Ising model on diluted graphs and strong amenability. Preprint (1999)
18. Janvresse, E., Landim, C., Quastel, J., Yau, H.T.: Relaxation to equilibrium of conservative dynamics I: zero-range process. Ann. of Prob., 27 (1), 325-360 (1999)
19. Lu, S.T., Yau, H-T.: Spectral gap and logarithmic Sobolev inequality for Kaasaki and Glauber dynamics. Commun. Math. Phys., 156, 399-433 (1993)
20. Martinelli, F.: Lectures on Glauber dynamics for discrete spin models. Proceedings of the Saint Flour summer school in probability theory 1997. Lecture Notes in Mathematics vol. 1717
21. Quastel, J.: Diffusion of Color in the simple Exclusion Process. Comm. Pure Appl. Math., XLV, 623 (1992)
22. Varadhan, S.R.S., Yau, H-T: Diffusive limit of lattice gases with mixing conditions. Preprint (1999)
23. Yau, H-T: Logarithmic Sobolev inequality for lattice gases with mixing conditions. Comm. Math. Phys., 181, 367 (1996)