Communications in Mathematical Physics

, Volume 125, Issue 1, pp 3–12 | Cite as

Stretched exponential decay in a kinetic Ising model with dynamical constraint

  • Herbert Spohn


We show that for the standard nearest neighbor spin-flip dynamics in one dimension with the constraint of constant energy the spin-spin correlation function decays as exp\([ - c\sqrt t ]\) for larget. We prove an upper and lower bound. The coefficientc of the lower bound is given as the solution of a variational problem and is conjectured to be exact.


Neural Network Statistical Physic Correlation Function Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Palmer, R., Stein, D., Abrahams, E., Anderson, P.W.: Models of hierarchically constrained dynamics for glassy relaxation. Phys. Rev. Lett.53, 958–961 (1984)Google Scholar
  2. 2.
    Fredrickson, G.H., Andersen, H.C.: Kinetic Ising model of the glass transition. Phys. Rev. Lett.53, 1244–1247 (1984)Google Scholar
  3. 3.
    Fredrickson, G.H.: Linear and nonlinear experiments for a spin model with cooperative dynamics. Ann. NY Acad. Sci.484, 185–205 (1987)Google Scholar
  4. 4.
    Skinner, J.L.: Kinetic Ising model for polymer dynamics. J. Chem. Phys.79, 1955–1963 (1983)Google Scholar
  5. 5.
    Budimir, J., Skinner, J.L.: Kinetic Ising model for polymer dynamics. II. J. Chem. Phys.82, 5232–5241 (1985)Google Scholar
  6. 6.
    Liggett, T.M.: Interacting particle systems. Berlin, Heidelberg, New York: Springer 1985Google Scholar
  7. 7.
    Holley, R.: Rapid convergence to equilibrium in one-dimensional stochastic Ising models. Ann. Probab.13, 72–89 (1985)Google Scholar
  8. 8.
    Huse, D., Fisher, D.: Dynamics of droplet fluctuations in pure and random Ising systems. Phys. Rev. B35, 6841–6846 (1987)Google Scholar
  9. 9.
    Sokal, A., Thomas, L.: Absence of a mass gap for a class of stochastic contour models. J. Stat. Phys.51, 907–947 (1988)Google Scholar
  10. 10.
    Kipnis, C., Olla, S., Varadhan, S.R.S.: Hydrodynamics and large deviation for simple exclusion processes (preprint)Google Scholar
  11. 11.
    DeMasi, A., Presutti, E., Scacciatelli, E.: The weakly asymmetric simple exclusion process. Ann. Inst. H. Poincaré (to appear)Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Herbert Spohn
    • 1
  1. 1.Theoretische PhysikLudwig-Maximilians-UniversitätMünchen 2Federal Republic of Germany

Personalised recommendations