By Dietrich Stauffer (auth.), H. Eugene Stanley, Nicole Ostrowsky (eds.)
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Additional info for Correlations and Connectivity: Geometric Aspects of Physics, Chemistry and Biology
R __ ' - 0" _ •••••••••• _ . ... . . . . . . . . . . . . . . . . , _ b) ur Fig. ) at Te if = -1 is fixed in a L=60 system (a) and (b) and if the damage is fixed on the boundary of a L = 100 system (c) for the 2d Ising model with heat bath dynamics. Figure (b) shows the evolution of cluster (a) after 38 time steps (from Ref. 7). 8) where the damage after a time t is different than zero and independent of the initial damage D(O); (III) A low temperature phase (T < T2 ) where the damage is different than zero but depends on the initial damage.
21 H. E. Stanley and N. ), Correlations and Connectivity, 21-33. © 1990 Kluwer Academic Publishers. 2 These clusters are in fact too large, representing both correlations and pure geometrical effects. As an example at T = 00 in a typical configuration clusters of parallel spins are present although there is total absence of correlations. To eliminate the pure geometrical effect a different definition of cluster was proposed5 for the Ising model and generalized to the q-state Potts model 6 The idea was based on a site bond correlated percolation model which was introduced as a model for a sol-gel transition.
De Arcangelis lectures). An equilibrium configuration is simulated and a clone made of the system. The central site is kept permanently up in the system but down in the clone: this site is permanently damaged. We monitor how the damage propagates with time. Whenever an update is performed it is done synchronously for site i of the system and the clone and the same random number is used for the update. The use of the same random number ensures that both the system and the clone interact with the JAN • POOLE • MAC ISAAC .