Information Technology Reference
In-Depth Information
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
/ν
.
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
/ν
)ln
L
. This is
the typical way to estimate
ν
. Due to the su
I
cient density ofdata we could find