Damage Spreading in Random Field Systems
We present extensive numerical results on the spreading of damage in random field systems. In this type of simulations two identical systems are subjected to the same thermal noise. Depending on the external parameters (e.g. temperature) an initially small perturbation (called the damage) will either heal or spread through the entire system. We are particularly interested in the influence of a random external field on these damage spreading phenomena. A recent mean-field theory for damage spreading in random field Ising models predicted that for low random field strength damage spreading is enhanced compared to the clean case since the random field strongly suppresses the magnetization. In contrast, a strong random field effectively pins the values of the spins in both systems reducing damage spreading. We have carried out Monte Carlo simulations of damage spreading in the random field Ising model for system sizes up to 2003 using different (bimodal, box and Gaussian) random field distributions. Our results qualitatively confirm the mean-field results. In contrast to the mean-field theory we find, however, that for intermediate and strong random field the long-time limit of the damage strongly depends on its initial configuration. These nonergodicities are signatures of a glassy state. By systematically exploring the possible damage configurations and their dependence on initial conditions and external parameters we show that damage spreading offers a valuable tool to characterize glassy behavior. We also discuss some computational subtleties of the damage spreading method which arise in connection with different update regimes.
T. Vojta and M. Schreiber, "Damage Spreading in Random Field Systems," Computer Physics Communications, vol. 121, Elsevier, Sep 1999.
The definitive version is available at http://dx.doi.org/10.1016/S0010-4655(06)70153-9
1998 Europhysics Conference on Computational Physics (1998: Sep. 2-5, Granada, Spain)
Keywords and Phrases
Computational methods; Computer simulation; Mathematical models; Monte Carlo methods; Perturbation techniques; Random processes; Damage spreading; Random field Ising model; Thermal noise; Statistical mechanics
International Standard Serial Number (ISSN)
Article - Conference proceedings
© 1999 Elsevier, All rights reserved.