The spontaneous generation of magnetic fields at high temperature in SU(2)-gluodynamics on a lattice
In a lattice formulation of the SU(2)-gluodynamics, the spontaneous generation of the chromomagnetic field at high temperature is investigated. The procedure to study this phenomenon is developed and Monte Carlo simulations are carried out on the lattices 2x8³, 4x8³ and 2x16³ at various temperatures...
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Demchik, V.I. Skalozub, V.V. 2017-01-07T09:24:04Z 2017-01-07T09:24:04Z 2007 The spontaneous generation of magnetic fields at high temperature in SU(2)-gluodynamics on a lattice / V.I. Demchik, V.V. Skalozub // Вопросы атомной науки и техники. — 2007. — № 3. — С. 111-115. — Бібліогр.: 15 назв. — англ. 1562-6016 PACS: 11.15.Ha, 11.10.Wx https://nasplib.isofts.kiev.ua/handle/123456789/110940 In a lattice formulation of the SU(2)-gluodynamics, the spontaneous generation of the chromomagnetic field at high temperature is investigated. The procedure to study this phenomenon is developed and Monte Carlo simulations are carried out on the lattices 2x8³, 4x8³ and 2x16³ at various temperatures. The χ²-analysis of the obtained data set indicates the presence of the spontaneously created magnetic field in the deconfinement phase. A comparison with the results of other approaches is done. Досліджено спонтанну генерацію хромомагнітного поля при високій температурі в гратковій формуліровці SU(2)-глюодинаміки. Розроблено процедуру для дослідження цього ефекта на гратці. Проведено моделювання методом Монте Карло на гратках 2x8³, 4x8³ та 2x16³ при різних температурах. χ²-аналіз отриманих даних вказує на наявність у фазі деконфайнменту магнітного поля, що народжується спонтанно. Проведено порівняння з результатами, отриманими у інших наближеннях Исследована спонтанная генерация хромомагнитного поля при высокой температуре в решеточной формулировке SU(2)-глюодинамики. Разработана процедура для исследования этого эффекта на решетке. Проведено моделирование методом Монте Карло на решетках 2x8³, 4x8³ и 2x16³ при различных температурах. χ²-анализ полученных данных указывает на существование в фазе деконфайнмента спонтанно рожденного поля. Проведено сравнение с результатами, полученными в других приближениях. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Elementary particle theory The spontaneous generation of magnetic fields at high temperature in SU(2)-gluodynamics on a lattice Спонтанна генерація магнітних полів при високій температурі в SU(2)-глюодинаміці на гратці Спонтанная генерация магнитных полей при высокой температуре в SU(2)-глюодинамике на решетке Article published earlier |
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| title |
The spontaneous generation of magnetic fields at high temperature in SU(2)-gluodynamics on a lattice |
| spellingShingle |
The spontaneous generation of magnetic fields at high temperature in SU(2)-gluodynamics on a lattice Demchik, V.I. Skalozub, V.V. Elementary particle theory |
| title_short |
The spontaneous generation of magnetic fields at high temperature in SU(2)-gluodynamics on a lattice |
| title_full |
The spontaneous generation of magnetic fields at high temperature in SU(2)-gluodynamics on a lattice |
| title_fullStr |
The spontaneous generation of magnetic fields at high temperature in SU(2)-gluodynamics on a lattice |
| title_full_unstemmed |
The spontaneous generation of magnetic fields at high temperature in SU(2)-gluodynamics on a lattice |
| title_sort |
spontaneous generation of magnetic fields at high temperature in su(2)-gluodynamics on a lattice |
| author |
Demchik, V.I. Skalozub, V.V. |
| author_facet |
Demchik, V.I. Skalozub, V.V. |
| topic |
Elementary particle theory |
| topic_facet |
Elementary particle theory |
| publishDate |
2007 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Article |
| title_alt |
Спонтанна генерація магнітних полів при високій температурі в SU(2)-глюодинаміці на гратці Спонтанная генерация магнитных полей при высокой температуре в SU(2)-глюодинамике на решетке |
| description |
In a lattice formulation of the SU(2)-gluodynamics, the spontaneous generation of the chromomagnetic field at high temperature is investigated. The procedure to study this phenomenon is developed and Monte Carlo simulations are carried out on the lattices 2x8³, 4x8³ and 2x16³ at various temperatures. The χ²-analysis of the obtained data set indicates the presence of the spontaneously created magnetic field in the deconfinement phase. A comparison with the results of other approaches is done.
Досліджено спонтанну генерацію хромомагнітного поля при високій температурі в гратковій формуліровці SU(2)-глюодинаміки. Розроблено процедуру для дослідження цього ефекта на гратці. Проведено моделювання методом Монте Карло на гратках 2x8³, 4x8³ та 2x16³ при різних температурах. χ²-аналіз отриманих даних вказує на наявність у фазі деконфайнменту магнітного поля, що народжується спонтанно. Проведено порівняння з результатами, отриманими у інших наближеннях
Исследована спонтанная генерация хромомагнитного поля при высокой температуре в решеточной формулировке SU(2)-глюодинамики. Разработана процедура для исследования этого эффекта на решетке. Проведено моделирование методом Монте Карло на решетках 2x8³, 4x8³ и 2x16³ при различных температурах. χ²-анализ полученных данных указывает на существование в фазе деконфайнмента спонтанно рожденного поля. Проведено сравнение с результатами, полученными в других приближениях.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/110940 |
| citation_txt |
The spontaneous generation of magnetic fields at high temperature in SU(2)-gluodynamics on a lattice / V.I. Demchik, V.V. Skalozub // Вопросы атомной науки и техники. — 2007. — № 3. — С. 111-115. — Бібліогр.: 15 назв. — англ. |
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2025-11-24T06:09:36Z |
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2025-11-24T06:09:36Z |
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| fulltext |
THE SPONTANEOUS GENERATION OF MAGNETIC FIELDS
AT HIGH TEMPERATURE IN SU(2)-GLUODYNAMICS ON A LATTICE
V.I. Demchik1 and V.V. Skalozub2
Dniepropetrovsk National University, Dniepropetrovsk, Ukraine;
1e-mail: vadimdi@yahoo.com;
2e-mail: skalozub@ff.dsu.dp.ua
In a lattice formulation of the SU(2)-gluodynamics, the spontaneous generation of the chromomagnetic field at
high temperature is investigated. The procedure to study this phenomenon is developed and Monte Carlo simula-
tions are carried out on the lattices 2x83, 4x83 and 2x163 at various temperatures. The χ2-analysis of the obtained
data set indicates the presence of the spontaneously created magnetic field in the deconfinement phase.
A comparison with the results of other approaches is done.
PACS: 11.15.Ha, 11.10.Wx
1. INTRODUCTION
Among interesting problems of modern cosmology
the origin of large-scale magnetic fields is intensively
attacked nowadays. Various mechanisms of the field
generation at different stages of the universe evolution
were proposed [1]. Basically they are grounded on the
idea of Fermi, Chandrasekhar and Zel'dovich that to
have the present day galaxy magnetic fields seed mag-
netic fields must be present in the early universe. These
fields had been frozen in a cosmic plasma and then am-
plified by some of the mechanisms of the field amplifi-
cation. One of the ways to produce seed fields is a spon-
taneous vacuum magnetization at high temperature T
[2,3,4,5]. Actually, this is an extension of the Savvidy
model for the QCD vacuum [6], proposed already at
T=0 and describing the creation of the Abelian
chromomagnetic fields due to a vacuum polarization, in
case of non-zero temperature. At zero temperature this
field configuration is unstable because of the tachyonic
mode in the gluon spectrum. At T ≠ 0, the possibility of
having strong temperature-dependent and stable mag-
netic fields was discovered [4]. The field stabilization is
ensured by the temperature and field dependent gluon
magnetic mass.
Another related field of interest is the deconfinement
phase of QCD. As it was realized recently, this is not
the gas of free quarks and gluons, but a complicate in-
teracting system of them. This was discovered at RHIC
experiments [7] and observed in either perturbative
[4,8] or nonperturbative [9] investigations of the vac-
uum state with magnetic fields at high temperature. In
Refs. [4,8] the spontaneous creation of the chromomag-
netic fields of order gB~g4T2 was observed in SU(2)-
and SU(3)-gluodynamics within the one-loop plus daisy
resummation accounted for. In Ref. [9] the fields of the
same order were observed in lattice simulations of two-
point correlators. In Ref. [10] the response of the vac-
uum to the influence of strong external fields at differ-
ent temperatures has been investigated and it was shown
that the confinement is restored by increasing the
strength of the applied field. These results stimulated
the present investigation. We are going to determine the
spontaneous creation of magnetic fields in lattice simu-
lations of SU(2)-gluodynamics. In contrast to the prob-
lems in the external field, in the case of interest the field
strength is a dynamical variable which values at differ-
ent temperatures have to be determined by means of the
minimization of the free energy. This procedure is not a
simple one as in continuum because the field strength
on a lattice is quantized. To deal with this peculiarity,
we consider magnetic fluxes on a lattice as the main
objects to be investigated. The fluxes take continuous
values, and therefore the minimization of the free en-
ergy in presence of magnetic field can be fulfilled in a
usual way. These speculations serve as an explanation
of the strategy of our calculations.
One of the methods to introduce a magnetic flux on
a lattice is to use the twisted boundary conditions
(t.b.c.) [11]. In this approach the flux is a continuous
quantity. So, in what follows we consider the free en-
ergy F(ϕ) with the magnetic flux ϕ on a lattice in the
SU(2)-gluodynamics and calculate its values at different
temperatures by means of Monte Carlo (MC) simula-
tions. We will show that the global minimum of F(ϕ) is
located at some non-zero value ϕmin dependent on the
temperature. It means the spontaneous creation of the
temperature-dependent magnetic fields in the decon-
finement phase.
2. MAGNETIC FIELDS ON A LATTICE
In perturbation theory, the value of the macroscopic
(classical) magnetic field generated inside a system is
determined by the minimization of the free energy func-
tional. The interaction with the classical field is intro-
duced by splitting the gauge field potential in two parts:
RAAA µµµ += , where describes a radiation field
and
RAµ
)0,1Hx,0,0(A =µ corresponds to the constant mag-
netic field directed along the third axis. However, on a
lattice, the direct detection of the spontaneously gener-
ated field strength by straightforward analysis of the
configurations, which are produced in the MC simu-
lations, seems to be problematic. Therefore, it is reason-
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2007, N3 (1), p. 111-115. 111
able to follow the approach used in the continuum field
theory.
First, let us write down the free energy density,
;
)0(
)(log)(
Z
ZF ϕ
ϕ −= (1)
({∫ −= )(exp)]([)( ϕϕϕ USDUZ )} . (2) ,( xUµ
Here, Z(ϕ) and Z(0) are the partition functions at finite
and zero magnetic fluxes, respectively; the link variable
U is the lattice analogue of the potential Aµ. The free
energy density relates to the effective action as follows,
)0()()( SSF −= ϕϕ , (3)
µ
where )(ϕS and )0(S are the effective lattice actions
with and without magnetic field, correspondingly.
To detect the spontaneous creation of the field it is
necessary to show that the free energy density has the
global minimum at a non-zero magnetic flux, . 0min ≠ϕ
In what follows, we use the hypercubic lattice
( ) with the hypertorus geometry; L3
st LL × st LL < t and
Ls are the temporal and the spatial sizes of the lattice,
respectively. In the limit of the temporal size
L
∞→sL
t is related to physical temperature. The one-plaquette
action of the SU(2) lattice gauge theory can be written:
∑ ∑
>
−=
x
W xTrUS
νµ
µνβ )](1[ 2
1 ; (4)
)()ˆ()ˆ()()( xUaxUaxUxUxU ++ ++= νµνµµν νµ , (5)
where β=4/g2 is the lattice coupling constant, g is the
bare coupling, Uµ(x) is the link variable located on the
link leaving the lattice site x in the µ direction, Uµν(x) is
the ordered product of the link variables.
The effective action S in (3) is the Wilson action
averaged over the Boltzmann configurations, produced
in the MC simulations.
The lattice variable Uµ(x) can be decomposed in
terms of the unity, I, and Pauli, σj, matrices in the col-
our space,
=+= )()()( 0 xUixIUxU j
j µµµ σ
−+−
++
=
)()()()(
)()()()(
3012
1230
xiUxUxiUxU
xiUxUxiUxU
µµµµ
µµµµ . (6)
The four components U are subjected to the nor-
malization condition . Hence, only
three components are independent.
)(xj
µ
(∑ Uj
j
µ 1)() =xUx j
µ
Since the spontaneously generated field is to be the
Abelian one, the Abelian parametrization of the lattice
variables is used to introduce the magnetic field,
−
= −− )()(
)()(
cossin
sincos
)( xixi
xixi
ee
ee
xU
µµ
µµ
θ
µ
χ
µ
χ
µ
θ
µ
µ
φφ
φφ
, (7)
where the angular variables are changed in the follow-
ing ranges θ, χ∈ [-π;+π), φ∈ [0;π/2).
The Abelian part of the lattice variables is repre-
sented by the diagonal components of the matrix and
the condensate Abelian magnetic field influences the
field θµ(x), only.
The second important task is to incorporate the mag-
netic flux in this formalism. The most natural way was
proposed by 't Hooft [11]. In his approach, the constant
homogeneous external flux ϕ in the third spatial direc-
tion can be introduced by applying the following t.b.c.:
),,,0(),, xxxUxxL = ; 321321t µ
),,0,(),,,( xxxUxxLxU = ; (8) 320320 s µµ
),0,,(),,,( xxxUexLxxU iϕ= ; 3
210210 s µ
10310 s µµ
)0,,,(),,,( xxxULxxxU = .
It could be seen, the edge links in all directions are
identified as usual periodic boundary conditions except
for the links in the second spatial direction, for which
the additional phase ϕ is added (Fig. 1). In the contin-
uum limit, such t.b.c. settle the magnetic field with the
potential Aµ(x)=(0,0,Hx1,0). The magnetic flux ϕ is
measured in angular units, . )2,0[ πϕ ∈
Fig. 1. The plaquette presentation of the twisted
boundary conditions
The lattice variables (in the Abelian parametrization)
in the presence of the magnetic flux ϕ are
=)(xU µ
−
= +−−
+
))()(()(
)())()((
cossin
sincos
xxixi
xixxi
ee
ee
µµµ
µµµ
ϕθ
µ
χ
µ
χ
µ
ϕθ
µ
φφ
φφ
,(9)
p
S
µµµµ
where ϕµ(x) = ϕ for the edge links at x = (x0, x1, Ls, x3)
with µ = 2 and ϕµ(x) = 0 for other links.
The total flux through the plane spanned by the
plaquettes p, which affects the edge links at
x=(x0, x1, Ls, x3) with µ = 2, is
∑
∈
+=Φ
planep
pg )( ϕθ , (10)
)()ˆ()ˆ()( xaxaxx νµνµ θνθνθθθ −+−++= . (11)
Eq. (10) is the lattice analogue of the flux in the contin-
uum . In this approach the variable
ϕ describes a flux through the whole lattice plane, not
just through an elementary plaquette.
∫=Φc Fd µνµνσ2
The t.b.c. for the components (9),
)(cos))()(cos()(0 xxxxU µµµµ φϕθ += ;
)(sin)(sin)(1 xxxU χφ= ; µµµ
)(sin)(sin)(2 xxxU χφ= ; µµµ
)(cos))()(sin()(3 xxxxU φϕθ += , (12)
112
read
ϕϕ µµµ sin)(cos)()( 300 xUxUxU −= , (13)
ϕϕ µµµ cos)(sin)()( 303 xUxUxU += (14)
for the edge links at x =(x0, x1, Ls, x3) with µ=2.
The relations (13) and (14) have been implemented
into the kernel of the MC procedure in order to produce
the configurations with the magnetic flux ϕ. In this case
the flux ϕ is accounted for in obtaining a Boltzmann
ensemble at each MC iteration.
3. MC SIMULATIONS AND DATA FITS
The MC simulations are carried out by means of the
heat bath method.
The spontaneous generation of magnetic field is the
effect of order ~g4 [4]. The results of MC simulations
show the comparably large dispersion. So, the large
amount of the MC data is collected and the standard χ2-
method for the analysis of data is applied to determine the
effect. We consider the results of the MC simulations as
observed “experimental data”.
The effective action depends smoothly on the flux ϕ
in the region ϕ~0. Therefore, the free energy density can
be fitted by the quadratic function of the flux ϕ,
2
minmin )()( ϕϕϕ −+= bFF . (15)
This choice is motivated also by the results obtained
already in continuum field theory [13] where it was de-
termined that free energy has a global minimum at ϕ 0.
The parametrization (15) is the most reasonable in this
case. It is based on the effective action accounting for the
one-loop plus daisy diagrams [13],
≠
−+= 2
2
22
2
22
log
48
11
2
)(
µπ
THHgHHF (16) 2
23
00
23
)]0([
12
1)(
3
1
Π−− TrTgH
π
,
having g2 and (g2)3/2 orders in coupling constant. Here, H
is field strength (flux ϕ~H), T is the temperature, µ is the
normalization point, is the zero-zero component
of the gluon polarazation operator calculated in the exter-
nal field at the finite temperature and taken at zero mo-
mentum. The value of β=3, which was used, corresponds
to a deep perturbation regime. So, a comparison with
perturbation results is reasonable. The systematic errors in
fitting function (15) could come from not taking into ac-
count the high-order diagrams in (16). However, as it is
well-known [15], the lack of an expansion parameter at
finite temperature starts from the three-loop diagram con-
tributions that is of g
)0(00Π
6 order and could not remove an ef-
fect derived in g2 and g3 orders. As the finite-size effects
are concerned, in the present investigation we just made
calculations for two lattices 2x83 and 2x163 and have
derived the same results for the ϕmin (as it will be seen
below). A more detailed investigation of this issue re-
quires much more computer resources, which were lim-
ited.
There are 3 unknown parameters, Fmin, b and ϕmin in
Eq.(16). The parameter ϕmin denotes the minimum posi-
tion of the free energy, whereas the Fmin and b are the free
energy density at the minimum and the curvature of the
free energy function, correspondingly.
The value ϕmin is obtained as the result of the minimi-
zation of the -function ),,( minmin
2 ϕχ bF
∑ −−+
=
i i
ii
FD
FbF
))((
))()(( 22
minmin2
ϕ
ϕϕϕ
χ , (17)
where ϕi is the array of the set fluxes and D(F(ϕi)) is the
data dispersion. It can be obtained by collecting the data
into the bins (as a function of flux),
∑
∈ −
−
=
bini bin
bini
i n
FFFD
1
)ˆ)(())((
2ϕϕ , (18)
where nbin is the number of points in the considered bin,
is the mean value of free energy density in the con-
sidered bin. As it is determined in the data analysis, the
dispersion is independent of the magnetic flux values ϕ.
The deviation of ϕ
binF̂
min from zero indicates the presence of
spontaneously generated field.
Fig. 2. χ2-fit of the free energy density on lattice
for β=3.0 (grey region describe the
ϕ
316×
.0min= at the 95% C.L.) 0022.0
0057.00069+−
The values of the generated fluxes ϕmin for different
lattices (at the 95% C.L.)
ϕmin 2x83 2x163 4x83
β=3 013.0
012.0019.0 +
− 0022.0
0057.00069.0 +
− 005.0
003.0005.0 +
−
β=5 011.0
010.0020.0 +
− - -
The fit results are given in Table 1. As one can see,
ϕmin demonstrates the 2σ-deviation from zero. The de-
pendence of ϕmin on the temperature is also in accordance
with the results known in perturbation theory: the in-
crease in temperature results in the increasing of the field
strength [4].
The fit for the lattice 2x163 at β=3.0 is shown in
Fig. 2. The maximum-likelihood estimate of F(ϕ) by the
whole data set is shown as the solid curve. In addition, all
ϕ values are divided into 10 bins. The mean values and
the 95% confidence intervals are presented as points for
each bin. The first 7 bins contain about 600-2000 points
per bin. The large number of points in the bins allow to
find the free energy F with the accuracy which substan-
tively exceeds the dispersion, 410~))(( −
iFD ϕ . It
makes possible to detect the effect of interest. As it is also
113
seen, the maximum-likelihood estimate of F(ϕ) is in a
good accordance with the bins pointed, because the solid
line is located in the 95% confidence intervals of all bins.
The 95% confidence level (C.L.) area of the parame-
ters b and ϕmin is represented in Fig. 3. The black cross
marks the position of the maximum-likelihood values of b
and ϕmin. It can be seen that the flux is positive deter-
mined. The 95% C.L. area becomes more symmetric with
the center at the Fmin, b and ϕmin when the statistics is in-
creasing. This also confirms the results of the fitting.
Fig. 3. The 95% C.L. area for the parameters ϕmin
and b, determining the free energy density dependence
on the flux ϕmin on lattice for β=3.0 3162×
4. DISCUSSION
The main conclusion from the results obtained is
that the spontaneously created temperature-dependent
chromomagnetic field is present in the deconfinement
phase of QCD. This supports the results derived already
in the continuum quantum field theory [4,12] and in
lattice calculations [9].
Let us first discuss the stability of the magnetic field
at high temperature. It was observed in Refs. [4,12] that
the stabilization happens due to the gluon magnetic
mass calculated from the one-loop polarization operator
in the field at temperature. This mass has the order
242122 ~)(~ TgTgHgmmagn as it should be because
the chromomagnetic field is of order TggH 221 ~)(
[4]. The stabilization is a non-trivial fact that, in princi-
ple, could be changed when the higher order Feynman
diagrams to be accounted for. Now we see that the sta-
bilization of the field really takes place.
Our approach based on the joining of calculation of
the free energy functional and the consequent statistical
analysis of its minimum positions at various tempera-
tures and flux values. This overcomes the difficulties
peculiar to the description of the field on a lattice. Here
we mean that the field strength on a lattice is quantized
and therefore a non-trivial tuning of the coupling con-
stant, temperature and field strength values has to be
done in order to determine the spontaneously created
magnetic field.
We also would like to note that in the present paper
the flux dependence on temperature remains not inves-
tigated in details. This is because of the small lattice
size considered. That restricts the number of points
permissible to study. However, at this stage we have
determined the effect of interest as a whole. Even at the
small lattice, one needs to take into consideration thou-
sands points of free energy (that corresponds to an
analysis of 5-10 millions MC configurations for differ-
ent lattices) to determine the flux value ϕmin at the 95%
C.L. In case of larger lattices this number and corre-
sponding computer resources should be increased con-
siderably. This problem is left for the future.
It is interesting to compare our results with that of in
Ref. [10] where the response of the vacuum on the ex-
ternal field was investigated. These authors have ob-
served in lattice simulations for the SU(2)- and SU(3)-
gluodynamics that the external field is completely
screened by the vacuum at low temperatures, as it
should be in the confinement phase. With the tempera-
ture increase, the field penetrates into the vacuum and,
moreover, increase in temperature results in existing
more strong external fields in the vacuum. On the other
hand, increase in the applied external field strength
leads to the decreasing of the deconfinement tempera-
ture. These interesting properties are closely related to
the studies in the present work. Actually, we have also
investigated the vacuum properties as an external field
problem when the field is described in terms of fluxes.
This was the first step of the calculations. The next step
was the statistical analysis of the minimum position of
free energy, in order to determine the spontaneous crea-
tion of the field. In fact, at the first step we reproduced
the results of Refs. [10] (in terms of fluxes).
Note that the present investigations also correspond
to the case of the early universe. They support our pre-
vious results on the magnetic field generation in the
standard model [13] and in the minimal supersymmetric
standard model [14]. As it was discussed by Pollock [5],
the field generated by this mechanism at the Planck era
might serve as a seed field to produce the present day
magnetic fields in galaxies.
We would like to conclude with the note that the de-
confinement phase of gauge theories is a very interest-
ing object to study. The temperature dependent mag-
netic fields living in this state influence various proc-
esses that should be taken into consideration to have an
adequate concept about them.
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СПОНТАННАЯ ГЕНЕРАЦИЯ МАГНИТНЫХ ПОЛЕЙ ПРИ ВЫСОКОЙ ТЕМПЕРАТУРЕ
В SU(2)-ГЛЮОДИНАМИКЕ НА РЕШЕТКЕ
В.И. Демчик, В.В. Скалозуб
Исследована спонтанная генерация хромомагнитного поля при высокой температуре в решеточной фор-
мулировке SU(2)-глюодинамики. Разработана процедура для исследования этого эффекта на решетке. Про-
ведено моделирование методом Монте Карло на решетках 2x83, 4x83 и 2x163 при различных температурах.
χ2-анализ полученных данных указывает на существование в фазе деконфайнмента спонтанно рожденного
магнитного поля. Проведено сравнение с результатами, полученными в других приближениях.
СПОНТАННА ГЕНЕРАЦІЯ МАГНІТНИХ ПОЛІВ ПРИ ВИСОКІЙ ТЕМПЕРАТУРІ
В SU(2)-ГЛЮОДИНАМІЦІ НА ГРАТЦІ
В.І. Демчик, В.В. Скалозуб
Досліджено спонтанну генерацію хромомагнітного поля при високій температурі в гратковій формуліро-
вці SU(2)-глюодинаміки. Розроблено процедуру для дослідження цього ефекта на гратці. Проведено моде-
лювання методом Монте Карло на гратках 2x83, 4x83 та 2x163 при різних температурах. χ2-аналіз отриманих
даних вказує на наявність у фазі деконфайнменту магнітного поля, що народжується спонтанно. Проведено
порівняння з результатами, отриманими у інших наближеннях.
115
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