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4.2 Determination of ε cr
In order to fix the crossing points ofcumulants we use 3rd order polynomial
fits to U L data for U L (0 . 590 , 0 . 620) taken as functions of ε cumulants. These
results are given in Fig. 2 .
0.620
0.620
Toom
asynchronous
Glaub e r
asynchronous
0.615
0.615
0.610
0.610
0.605
0.605
L=20
L=40
L=60
L=80
L=100
fit to 3rd order
polynomial
0.600
0.600
0.595
0.595
0.590
0.590
0.716
0.717
0.718
0.719
0.720
0.721
0.8645
0.8650
0.8655
0.8660
0.8665
0.8670
0.620
0.620
Glaub e r
synchronous
Toom
synchronous
0.615
0.615
0.610
0.610
0.605
0.605
0.600
0.600
0.595
0.595
0.590
0.590
0.8205
0.8210
0.8215
0.8220
0.8225
0.8230
0.654
0.655
0.656
0.657
0.658
0.659
noise ε
noise ε
Fig. 2. Estimates of the transition points by Binder's method. Binder's cumulants (10)
versus ε are presented for different system sizes 20 ≤ L ≤ 100. Symbols correspond to
raw data, lines to 3rd order polynomial fits.
Notice that the values of U L at the crossing points are in remarkable agree-
ment with the ones expected for Ising system.
4.3 Finite-Size Scaling Analysis to Determine ν
The properties oflogarithmic derivatives ofhigher moments ofmagnetization:
ε log |m| L , ε log m L , ε log m L at critical point ε cr scales with L as L 1 .
Moreover, some related quantities defined as [21]:
V 2 =2[ m 2 ] [ m 4 ] , 4 = (4[ m ] [ m 4 ]) / 3 , 6 =2[ m ] [ m 2 ]
(13)
where [ m n ]=ln ε m L at critical point ε cr depend on L like (1 )ln L . This is
the typical way to estimate ν . Due to the su I cient density ofdata we could find
 
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