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arXiv:cond-mat/9807229 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Differences between regular and random order of updates in damage-spreading simulations

Thomas Vojta, Michael Schreiber

Published Dec 1, 1998• 10 citations
arXivHTMLPDF

Abstract

We investigate the spreading of damage in the three-dimensional Ising model by means of large-scale Monte Carlo simulations. Within the Glauber dynamics we use different rules for the order in which the sites are updated. We find that the stationary damage values and the spreading temperature are different for different update order. In particular, random update order leads to larger damage and a lower spreading temperature than regular order. Consequently, damage spreading in the Ising model is nonuniversal not only with respect to different update algorithms (e.g., Glauber vs heat-bath dynamics) as already known, but even with respect to the order of sites.

DOI
10.1103/physreve.58.7998

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Journal of Physics A Mathematical and General•May 7, 1990•36 citations
We investigate the spreading of damage in the three-dimensional Ising model by means of large-scale Monte Carlo simulations. Within the Glauber dynamics we use different rules for the order in which the sites are updated. We find that the stationary damage values and the spreading temperature are different for different update order. In particular, random update order leads to larger damage and a lower spreading temperature than regular order. Consequently, damage spreading in the Ising model is nonuniversal not only with respect to different update algorithms (e.g., Glauber vs heat-bath dynamics) as already known, but even with respect to the order of sites.
The authors study damage spreading in the Ising model, on a square lattice, by a Monte Carlo approach, using a general 'f-dynamics' (0<or=f<or=1) which reproduces, for f=0 the well known heat-bath dynamics and for f=1 Glauber dynamics. They find, for initially small damage, a critical value f c =0.50+or-0.03 as the threshold for damage spreading. For f c <f<or=1 the damage is non-zero only for T c <T<T 0 (f), where T c is the usual critical temperature and T 0 (f) rises with f like T 0 (f)-T c infinity (f-f c ) alpha ( alpha =0.83+or-0.08). For T c <or=T the damage D(T,f) seems to satisfy the scaling relation D(T,f) approximately mod 1n(f-f c ) mod -1 T((1-T c /T)/(f-f c ) alpha ).
We investigate how a quenched random field influences the damage-spreading transition in kinetic Ising models. To this end we generalize a recent master equation approach and derive an effective field theory for damage spreading in random-field systems. This theory is applied to the Glauber Ising model with a bimodal random-field distribution. We find that the random field influences the spreading transition by two different mechanisms with opposite effects. First, the random field favours the same particular direction of the spin variable at each site in both systems which reduces the damage. Second, the random field suppresses the magnetization which in turn tends to increase the damage. The competition between these two effects leads to a rich behaviour.
Using information of the ground-state topology we show that the damage spreading technique unveils ferromagnetic order in the three-dimensional ± J Edwards-Anderson spin glass model. With spin-flipping dynamics damage spreads for temperatures larger than T g , the glass transition temperature. With spin-orienting dynamics and for temperatures in T g < T < T d , damage spreads over a finite region of the system, composed of finite clusters of ferromagnetic character. T d is the spin-orienting damage critical temperature, which is of the same order as the critical temperature of the ferromagnetic Ising model, T c . The present results allow for an interpretation within a single framework of known —and sometimes puzzling— results, giving an intuitive picture for growing order in spin glasses.
The computer simulations of the critical dynamics of the structurally disordered three-dimensional Ising model are performed by the damage spreading method. For the systems with spin densities p = 0.6 and 0.8, we calculate the critical temperature and dynamic critical exponent z characterizing the behavior of relaxation properties near the critical point. The analysis of the results demonstrates the nonuniversality of the critical dynamics in the disordered Ising model. To interpret such dynamics, we introduce the concept of two universal types of critical behavior corresponding to weak and strong disorder, respectively.