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magnetization |m| and susceptibility
χ
(L=100)
400
1.0
Glauber
asynchronous
|m|
χ
0.8
Toom
synchronous
300
0.6
200
0.4
Toom
asynchronous
100
Glauber
synchronous
0.2
0
0.0
0.6
0.7
0.8
0.9
1.0
noise
ε
Fig. 1.
Noise dependence of the macroscopic observables of TCA and GCA. Magneti-
zation
|m
L
|
(right scale) and susceptibility
χ
L
(left scale) for all systems considered in
case of lattice
L
= 100.
where
ε
cr
is the infinite-size transition point. Preliminary identification of
ε
cr
can be made by locating the crossing point ofthe ourth-order cumulants of
magnetization (10). The common value of
U
L
at the crossing point is a univer-
sal number determining a universality class also. The Ising kinetic systems are
characterized by
U
Ising
∈
(0
.
610
,
0
.
612) [14].
4 Results
4.1 Error Analysis
Since the susceptibility measures the variation ofthe order parameter, i.e., mag-
netization, one can draw conclusions about the statistical errors in our simula-
tions from Fig. 1. Standard deviation errors are smaller for other quantities. In
the interval where a system is close to the phase transition extra simulations
(repeated runs and
/
or moving
ε
a little) were performed to assure the validity
ofthe values. The procedure ofextracting critical exponents needs estimates for
derivatives. Usually, numerical estimates ofa derivative consist in approximat-
ing the derivative by a finite difference taken between two points neighboring
to
ε
cr
. This method, however, is di
I
cult to control in case ofnoisy data. More-
over, it is sensitive to statistical errors ofthe values oforiginal data. Instead, we
choose to fit experimental data with linear functions. The quality of the fits is
estimated by the standard correlation coe
I
cient
r
2
. In the following, all linear
fits together with the corresponding correlation coe
I
cients, calculated by the
computer program SigmaPlot2000 by Jandel Scientific, are
r
2
>
0
.
90.
