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Complex Ising
1
About
1.1
Usage
1.2
Render book
1.3
Preview book
2
Lagrangian
2.1
Metropolis update
2.2
Correlators
3
Odd lattice simulations
3.0.1
problem with L-1 multiple of 6
4
Hopping expansion Cross-check
4.0.1
Haar measure
4.0.2
Partition function for small hopping parameter
κ
4.0.3
Energy
4.0.4
Numerical test
4.0.5
g term
4.0.6
Numerical integration g term
5
Renormalized couplings
6
g=0
6.1
magn
6.2
imag g0
7
fits g0
7.1
Mass
7.2
fit
a
from perturbative expansion
7.3
Luescher analysis
7.3.1
M
L
in zeta func and
M
∞
as normalization
7.3.2
Using
M
∞
7.3.3
no correction
7.4
fitting the energy levels
7.4.1
1 level 1 par
7.5
QC3 fit g0
7.5.1
no resonace antsaz g0 kcot1par
7.5.2
resonace antsaz g0
7.6
GEVP E2 g0
7.7
GEVP E3 g0
7.8
m
2
0
=
-1.267
m
2
1
=
-0.55
7.9
Summry energy level g=0
8
g=0.1
8.1
GEVP E3 g0.1
9
g=0.5
9.1
GEVP E3 g0.5
10
g=1
10.1
GEVP E3 g1
11
g=2
11.1
GEVP E3 g2
12
g=5
12.1
GEVP E2 g5
12.2
GEVP E3 g5
13
Summry energy level g5
13.0.1
Mass
13.0.2
two particle
13.0.3
a0
13.0.4
Three particle
13.0.5
p1 level
14
fits g5 small L
14.1
Mass
14.2
fit
a
from perturbative expansion
14.3
Luescher analysis
14.3.1
M
L
in zeta func and
M
∞
as normalization
14.3.2
Using
M
∞
14.4
fitting the energy levels
14.5
QC3 fit small L
14.6
QC3 fit 3par
14.7
Poly fit E3
15
fits g5
15.1
Mass
15.2
fit
a
from perturbative expansion
15.3
Luescher analysis
15.3.1
M
L
in zeta func and
M
∞
as normalization
15.3.2
Using
M
∞
15.4
fitting the energy levels
15.5
QC3 fit
15.5.1
kcot 1 par
15.5.2
no coupling
16
fits g5 large L
16.1
Mass
16.2
fit
a
from perturbative expansion
16.3
Luescher analysis
16.3.1
M
L
in zeta func and
M
∞
as normalization
16.3.2
Using
M
∞
16.4
fitting the energy levels
16.5
QC3 fit g5 largeL
16.5.1
kcot 1 par kiso 2 par
16.5.2
kcot 1 par kiso 3 par
16.5.3
kcot 1 par kiso 2 par cov
16.5.4
kcot 1 par kiso 3 par cov
16.5.5
kcot 1 par kiso 3 par cov 200 confs
16.5.6
kcot 1 par kiso 3 par cov 400 confs
16.5.7
no resonace antsaz g5 kcot1par
17
g10
17.1
GEVP E3 g10
17.2
GEVP E2 g10
18
fits g10
18.1
Mass
18.2
fit
a
from perturbative expansion
18.3
Luescher analysis
18.3.1
M
L
in zeta func and
M
∞
as normalization
18.3.2
Using
M
∞
18.3.3
no correction
18.4
fitting the energy levels
18.4.1
fitting the energy levels 1 level 1 par
18.5
Poly fit E3 g10
18.6
QC3 fit 3par
18.7
fitting two and three together g10
18.7.1
kcot 1 par
18.7.2
kcot 1 kis0 3 par covariance
18.7.3
kcot 1 kis0 2 par covariance
18.8
no resonace antsaz g10
18.8.1
no resonace antsaz g10 kcot1par
18.8.2
kcot 1 par kiso 2 par
19
g20
19.1
GEVP E3 g20
20
fits g20
20.1
Mass
20.2
fit
a
from perturbative expansion
20.3
Luescher analysis
20.3.1
M
L
in zeta func and
M
∞
as normalization
20.3.2
Using
M
∞
20.3.3
no correction
20.4
fitting the energy levels
20.5
QC3 fit g20
20.5.1
kcot 1 par
20.5.2
kcot 1 par kiso 2 par
20.5.3
kcot 1 par kiso 2 par and covariance
20.5.4
kcot 1 par kiso 3 par and covariance
21
g=50
21.1
GEVP E3 g50
21.2
Summry energy level g=50
22
g=400
22.1
GEVP E3 g400
22.2
Summry energy level g=400
23
g=800
23.1
GEVP E3 g800
24
g=1600
24.1
GEVP E3 g1600
24.2
Summry energy level g=1600
25
hadron checks
25.0.1
Reading the configuration
25.0.2
GEVP
25.0.3
Effective mass
25.0.4
correlators
25.1
g200 hadron
25.1.1
Reading the configuration
25.1.2
GEVP
25.1.3
Effective mass
25.1.4
correlators
25.1.5
Comparing off diagonal GEVP g50 g200
25.2
g1600 hadron
25.2.1
Reading the configuration
25.2.2
GEVP
25.2.3
Effective mass
25.2.4
correlators
26
g=0.5 deriv
26.1
GEVP E3 g0.5 deriv
27
g=1 deriv
27.1
GEVP E3 g1 deriv
28
g=2 deriv
28.1
GEVP E3 g2 deriv
29
compare E3 g
29.0.1
m0= -1.2 m1= -0.55E3_0 (g0) = 0.97445(59)
χ
2
/
d
o
f
=
0.45157
30
Summry energy level compare
30.0.1
Mass
30.0.2
two particle
30.0.3
a0
30.0.4
Three particle
30.0.5
p1 level
31
Parameters dependence on g
31.0.1
2par Kiso 1 Kcot
31.0.2
3par Kiso 1 Kcot
31.1
Pole in
M
3
32
integral eq
32.0.1
Parametrization of the resonance
32.1
g5_largeL
32.1.1
g5_largeL closer to the pole
32.1.2
g5_largeL plus const
32.1.3
g5_largeL Breit-Wigner
32.1.4
g5_largeL F fit
32.2
g10
32.2.1
g10 closer to the pole
32.2.2
g10 plus const
32.2.3
g10 Breit-Wigner
32.2.4
g10 F fit
32.3
g20
32.3.1
g20 closer to the pole
32.3.2
g20 plus const
32.3.3
g20 Breit-Wigner
32.3.4
g20 F fit
References
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Complex
ϕ
4
Chapter 30
Summry energy level compare
30.0.1
Mass
15
20
25
0.22
0.24
0.26
0.28
0.3
0.32
g,m0,m1
0 -1.2 -0.55
0 -1.25 -0.55
0 -1.267 -0.55
10 -1.23 -0.36
10 -1.23 -0.37
10 -1.25 -0.5
20 -1.204 -0.37
20 -1.23 -0.37
40 -1.16 -0.34
40 -1.164 -0.34
40 -1.165 -0.34
40 -1.166 -0.34
40 -1.175 -0.34
40 -1.18 -0.34
40 -1.199 -0.34
40 -1.2 -0.34
40 -1.201 -0.35
40 -1.202 -0.36
40 -1.203 -0.37
40 -1.2035 -0.37
40 -1.204 -0.37
5 -1.2 -0.55
5 -1.242 -0.38
5 -1.267 -0.55
5_largeL -1.2413 -0.38
L
E (one particle)
plotly-logomark
30.0.2
two particle
15
20
25
−0.5
0
0.5
1
g,m0,m1
0 -1.2 -0.55
0 -1.25 -0.55
0 -1.267 -0.55
10 -1.23 -0.36
10 -1.23 -0.37
10 -1.25 -0.5
20 -1.204 -0.37
20 -1.23 -0.37
40 -1.16 -0.34
40 -1.164 -0.34
40 -1.165 -0.34
40 -1.166 -0.34
40 -1.175 -0.34
40 -1.18 -0.34
40 -1.199 -0.34
40 -1.2 -0.34
40 -1.201 -0.35
40 -1.202 -0.36
40 -1.203 -0.37
40 -1.2035 -0.37
40 -1.204 -0.37
5 -1.2 -0.55
5 -1.242 -0.38
5 -1.267 -0.55
5_largeL -1.2413 -0.38
0 -1.2 -0.55 p1
0 -1.25 -0.55 p1
0 -1.267 -0.55 p1
10 -1.23 -0.36 p1
10 -1.23 -0.37 p1
10 -1.25 -0.5 p1
20 -1.204 -0.37 p1
20 -1.23 -0.37 p1
40 -1.16 -0.34 p1
40 -1.164 -0.34 p1
40 -1.165 -0.34 p1
40 -1.166 -0.34 p1
40 -1.175 -0.34 p1
40 -1.18 -0.34 p1
40 -1.199 -0.34 p1
40 -1.2 -0.34 p1
40 -1.201 -0.35 p1
40 -1.202 -0.36 p1
40 -1.203 -0.37 p1
40 -1.2035 -0.37 p1
40 -1.204 -0.37 p1
5 -1.2 -0.55 p1
5 -1.242 -0.38 p1
5 -1.267 -0.55 p1
5_largeL -1.2413 -0.38 p1
0 -1.2 -0.55 A1
0 -1.25 -0.55 A1
0 -1.267 -0.55 A1
10 -1.23 -0.36 A1
10 -1.23 -0.37 A1
10 -1.25 -0.5 A1
20 -1.204 -0.37 A1
20 -1.23 -0.37 A1
40 -1.16 -0.34 A1
40 -1.164 -0.34 A1
40 -1.165 -0.34 A1
40 -1.166 -0.34 A1
40 -1.175 -0.34 A1
40 -1.18 -0.34 A1
40 -1.199 -0.34 A1
40 -1.2 -0.34 A1
40 -1.201 -0.35 A1
40 -1.202 -0.36 A1
40 -1.203 -0.37 A1
40 -1.2035 -0.37 A1
40 -1.204 -0.37 A1
5 -1.2 -0.55 A1
5 -1.242 -0.38 A1
5 -1.267 -0.55 A1
5_largeL -1.2413 -0.38 A1
L
E2 (two particles)
plotly-logomark
30.0.3
a0
15
20
25
−1.5
−1
−0.5
0
0.5
1
1.5
g,m0,m1
0 -1.2 -0.55
0 -1.25 -0.55
0 -1.267 -0.55
10 -1.23 -0.36
10 -1.23 -0.37
10 -1.25 -0.5
20 -1.204 -0.37
20 -1.23 -0.37
40 -1.16 -0.34
40 -1.164 -0.34
40 -1.165 -0.34
40 -1.166 -0.34
40 -1.175 -0.34
40 -1.18 -0.34
40 -1.199 -0.34
40 -1.2 -0.34
40 -1.201 -0.35
40 -1.202 -0.36
40 -1.203 -0.37
40 -1.2035 -0.37
40 -1.204 -0.37
5 -1.2 -0.55
5 -1.242 -0.38
5 -1.267 -0.55
5_largeL -1.2413 -0.38
L
$a_0$
plotly-logomark
30.0.4
Three particle
15
20
25
0.7
0.75
0.8
0.85
0.9
0.95
g,m0,m1
0 -1.2 -0.55
0 -1.25 -0.55
0 -1.267 -0.55
10 -1.23 -0.36
10 -1.23 -0.37
10 -1.25 -0.5
20 -1.204 -0.37
20 -1.23 -0.37
40 -1.16 -0.34
40 -1.164 -0.34
40 -1.165 -0.34
40 -1.166 -0.34
40 -1.175 -0.34
40 -1.18 -0.34
40 -1.199 -0.34
40 -1.2 -0.34
40 -1.201 -0.35
40 -1.202 -0.36
40 -1.203 -0.37
40 -1.2035 -0.37
40 -1.204 -0.37
5 -1.2 -0.55
5 -1.242 -0.38
5 -1.267 -0.55
5_largeL -1.2413 -0.38
L
E3 (three particles)
plotly-logomark
15
20
25
2.4
2.6
2.8
3
3.2
3.4
3.6
g,m0,m1
(0 -1.2 -0.55,1)
(0 -1.25 -0.55,1)
(0 -1.267 -0.55,1)
(10 -1.23 -0.36,1)
(10 -1.23 -0.37,1)
(10 -1.25 -0.5,1)
(20 -1.204 -0.37,1)
(20 -1.23 -0.37,1)
(40 -1.16 -0.34,1)
(40 -1.164 -0.34,1)
(40 -1.165 -0.34,1)
(40 -1.166 -0.34,1)
(40 -1.175 -0.34,1)
(40 -1.18 -0.34,1)
(40 -1.199 -0.34,1)
(40 -1.2 -0.34,1)
(40 -1.201 -0.35,1)
(40 -1.202 -0.36,1)
(40 -1.203 -0.37,1)
(40 -1.2035 -0.37,1)
(40 -1.204 -0.37,1)
(5 -1.2 -0.55,1)
(5 -1.242 -0.38,1)
(5 -1.267 -0.55,1)
(5_largeL -1.2413 -0.38,1)
L
E3/M
plotly-logomark
30.0.5
p1 level
15
20
25
0.7
0.8
0.9
1
1.1
1.2
1.3
g,m0,m1
0 -1.2 -0.55
0 -1.25 -0.55
0 -1.267 -0.55
10 -1.23 -0.36
10 -1.23 -0.37
10 -1.25 -0.5
20 -1.204 -0.37
20 -1.23 -0.37
40 -1.16 -0.34
40 -1.164 -0.34
40 -1.165 -0.34
40 -1.166 -0.34
40 -1.175 -0.34
40 -1.18 -0.34
40 -1.199 -0.34
40 -1.2 -0.34
40 -1.201 -0.35
40 -1.202 -0.36
40 -1.203 -0.37
40 -1.2035 -0.37
40 -1.204 -0.37
5 -1.2 -0.55
5 -1.242 -0.38
5 -1.267 -0.55
5_largeL -1.2413 -0.38
L
E3 (three particles)
plotly-logomark