SCIENTIFIC ABSTRACT TYABLIKOV, S.V. - TYABLIKOV, S.V.

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• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

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USSR Magnetism Antiferramagnetism F
Abs Jour : Ref Zhur - Fizika, No 4, 1957~ No 9541
Author : Tyablicov, S.V.
Inst : 1ftttIemuttni-*a4tAtute imeni Steklov, A-.adenrj of Sciences
USSR, Moscow
Title : Concerning the Theory of Antiferromagnetium
Ori g Pub : Fiz. metallov i metallovedeniye, 1956, 2, No 2, 193-205
Abstract : With the aid of one of the variants of the method of ap-
proximate second quantization, the author computes the ma-
gaetization. and susceptibility of an antiferromagnetic as
a function of the temperature and of the external magnetic
field. For weak fields, the results are in agreement with
those obtained by Hulten (Hulten, L., Proceedings Royal A-
cademy of Sciences, Amsterdam, 1936, 39, 190):
+ AVH I
Card 1/2

USSR / Magrietisms Anti-ferrcmagnetiam
Abs JOur : Ref Zhur - Fizika, No 4, 1957, No 9541
Abstract : where c is the certain constant and J1. is a quantity that
characterizes the exchange interaction of the anti-parallel
spins. In stronger fields one obtains the following formu-
las for the magnetization:
Al + e-, T'/'
and:
M e-, 7-
Card 2/2

%F tA
L I
USSR Magnetism Ferromagnetism
Abs Jour t Ref Zhur - Fizika, No 4, 1957, No 9504
Auth or : Tyablikov., S.V., Gusev,, A.A.
F-4
Inst 3'*MaTfie-Rari-cs Institute imeni V.A. Steklov, Academy of Scien-
ces USSR; **Foreign Literature Press.
Title IDependence of the Constants of Magnetic Anisotropy of Cubic
Crystals on the Temperature and on the Field.
Orig Pub Fiz. metallov i metallovedeniye, 1956, 2, No 3, 385-390
Abstract Using the method of approximate second quantization, the au-
thors calculate the dependence of the magnetic-anisotropy
constants of crystals of the cubic system on the temperatu-
re and on the external magnetic field under the-assumption
that the terms of the Harliltonian of the system, responsible
for the anisotropy, can be represented in the form of the
fourth form relative to the spin operators.
Card : 1/1

V
USSR Magnetism , Ferrites F - .6
Abs Jour Ref Zhur - Fizika, No 4, 1957, No 9549
Author Tya ilikcryS.V, .
Inst Mathematics Institute imeni V.A. Steklov) ucadevj of Sciences
USSR, Moscow
Title Calculation of Magnetization of Ferrites as Function of the
Temperature and Fields.
Orig Pub : Fiz. metallov i metallovedeniye, 1956, 3, No 1, 3-10
Abstract : The author calculates the dependence of the magnetization
on the temperature and on the field for ferr gnetic semi-
conductors, which are represented in accordance with the
Neel model as an aggregate of two ferromagnetic lattices
with non-vanishing total magnetic inserted in eAbh other.
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14 V\ L-1 V I_J , V
-SUDJECT, USSR / PHYSICS CARD 1 / 2 PA - 1390
AUTHOR TOLMACEV, V.V., TJAUIKOV, S.V.
TITLE A Method for the Computation of the Statistical Sums for Ferro-
magnetics, in Consideration of the Restrictions Imposed upon the
Filling Numbers of the Spin Waves.
PERIODICAL Doxl.Akad.Nauk, 108, fase. 6, 1029-1031 (1956)
Issued: 9 / 195-C- reviewed: 10 / 1956
The present representation of this method takes into account that the projec-
tion of the spin of every atom (in _~ /2 units) assumes only the two values
+ 1 if one electron corresponds to each atom.
it first the HAMILTONIAN of the ferromagneticum is written down, after rhich
one passes from spin operators to BOSE operators. Also on this occasion one
electron is supposed to correspond to each atom. The HAMILTONIAN in this new
variable is written down as a sum of three summands E + X 1 + 11~1> , and
each summand is explicitly given. The equations Je Est for the deter-
mination of eigenfunctions and eigenvalues are to be inve igated only within
the space of the filling-up numbers n f - 00. However, in order to simplify
further computations, this equation is examined in all spaces of all possible
filling-up numbers; the restriction to n f - 0,1 is taken into account by the
introduction of an operator P T' [ A (nf) + A (nf-1 Here L (n)- 1
M ) 3 -
and A n - 0 is true for n-0 and n ~ 0 respectively. This operator P projects

.Dokl.Akad.Nauk, 108, faso. 6, 1029-1031 (1956) CARD 2 / 2 PA - 1,390
the functions applying within the space of all possible filling-up functions
on to the functions in the space with n f - 0j;1,
In zero-th approximation Z. W Sp(e"411 o/0) is true for the sum of states, on
which occasion the trace is extended to the space of the numbers n f - 0~!I
zo - Sp(P exp [ - :k' /9 ] )is true in the space of all possible filling -up
0
numbers. The computation of Z 0 is simplified considerably by making use of
an orthonormalizing systeml the rather complicated expression found is explic-
itly given. There follows herefrom at low temperatures
Z0 11 + L e-E(-)/G.
(v)
According to information received from N~N.BOGOLJEBOV similar ideas were al~
ready developed by DYSON in manuscripts meanwhile received while the pregent
work was being printed.
INSTITUTION: Mathematical Institute V.A.STEKLOV of the Academy of Science
in the USSR

SUBJE-CT: USSRIPhysics of Magnetic Phenomena 4M-13/23
AUTHORS: Bogoly-ubov, N.H. and Tyablikov, S.V.
TITLE: Approximate Methods of Secondary Quantization in the Quantum
Theory of Magnetism (Priblizhennyye metody vtorichnogo kvanto-
vaniya v kvantovoy teorii magnetizma)
PERIODICALt Izvestiya Akademii Nauk SSSR, Seriya Fizicheskaya, 1957, Vol 21,
#6, pp 849-853 (USSR)
ABSTRACT: The problem of a rigorous calculation of the energetic spectrum
for ferronagnetic materials is extremely difficult, and there-
fore, approximate methods were devised for its treatment.
These methods enter into two stages of calculationst
1. The constructing of a simplified "model" Hamiltonian which
conveys characteristic peculiarities of a studied dynamic system;
2. The formulation of an approximate method for such a simpli-
fied Hamiltonian.
The starting point in constructing the simplified Hamiltonian
is a rigorous Hamiltonian of the 6yetem in secondary quantiza-
tion presentatione However, only ajart of the atomic wave func-
Card 1/3 tions ia accounted in actual calcul ions, following the ideas

4&~13/23
TITLEi Approximate Methods of Secondary Quantization in the '%-Uantum
Theory of Magnetism (Priblizhennyye metody vtorichnogo kvanto-
vaniya v kvantovoy teorii magnetizma)
of Ritz.
Then an approximate method is applied to this simplified Hamil-
tonlan, The resulting form coincides with the form of the
second variation in the quasi-olassical treatmont.
Since in this approximation the Hamiltonian Is a quadratic forr.
of Bose-operators# its diagonalization does not present dny
difficulties,
This method of calculating the energetic spectrum of weakly-
excited states was applied by the authors to the theory of fer-
romagnetic materials and led to the known results in the Bloch
theory of spin waves. When spin-spin and spin-orbital interac-
tion terms are included into the Hamiltonian, it is possible
to calculate the temperature- and field intensity-dependence
of the magnetic anisotropy (4, 5) and the magnetostriction (6).
The methods developed were also applied to the theory of anti-
ferromagnetism (2).
Card 2/3 There are 11 references,10 of which are Russian.

4"413M
TITLEt Approximate Methods of Secondary Quantization in the Quantum
Theory of Magnetism (Priblithennyy matody vtorichnogo kyanto-
vaniya v kvantovoy toorii magnotiz:a)
ASSOCIATIONt Physical Deyar%ment of the Noskwt State University imeni.
Lomonosov.
PRESENTED BYt
SUBMITTEDs No date indicated,
AVAILABLE% At the Library of Congress,
Card 3/3

SUBJECT: USSR!Physics of Magneti.,; Phenorriena
AUTHORS: Gusev, A.A, and Tyablikov, S.V.
TITLE: On Dependence of Magnetic Anisotropy Constants on Temper; ture,
and Field Intenaity in Cubic Cry.9tale (0 zavislmo3tl Poni;tant
magnitnoy nni7otropl,l kubichoaklkh kriatpiLlov f')t temporntu'r"', i
polya)
PERIODICALt Izvestiya Akademit Nauk SSSR, Weriya Fizichuskaya, 1957, Vc.). -71,
#6, p 887 (U3SR)
ABSTRACT: The Hamiltonian of a system of electrons cauaing ferromagnetism
in the Heitler-London model can be presentel as - serieo ex-
panded by even power3 of spin operntors,
When the cubic symmetr- of the lattice is taken into account tip
to the terms of the fourth power, it is poosible, by !-eans of an
aprroximate second quantization method, to determine the energe-
tic spectrums of the system, to calculate the free energy an-i
to find formulae for the constants Of Magnetic atLisCltrOpy Rc;
functions of temperature and magnetic field interin~-.J-_
An approximate expression is given for the first const.Rnt Of
Card 112 magnetic anisotropy in a cubic ferromagnetic monocrystal.

TITLE: On dependence of ~'agnetic Anisotropy Constants
and Field Tntmn,-,4-tj in Cololc Crynti-In !G zhvitsa.,~,!,itt
mogrOtTloy anizutruptl kiJichenkikh kristallov ot,
poly&)
This raport in wnu rubll3hed in 701 21
P 365, No refQrpnces' nre cited,
ASSOCIATION: Moskva State University imeni Y.om.~Incocv.
PRESE"TTD BY:
SUBMITTED: No date indicated,
AVAILABLEi At the Library of Congreas,
Card 2/2

TYABLIKOV, Serge;~'Viadiirdmvich, GU~~V, I-I.A., red,
[Mett,c,dn in the quantuz theory of zag.,tim' Xetcai
kvantovol teoril magnetima. Mos.Kva, Nau~ka, 1905.
334' P. (MINk 16:4)

KRYMOV, Yu.g.~ TVERSKOY, B.A.
Changes in the energy of varticles ir. a diDole field -4-
transilvion3 between varloua drive xurfaces .. Geomag. -, aver.
4 no.2:397-399 Mr-Ap 164. (MIRA 17:4)
1. MoBkovskiy gosudarstvennyy universitet Institut yadernoy
fiziki.

20-114--6-20/54
AUTHORSt Tyablikov, S. V., Tolmachev, V. V.
TITLEs Distribution Functions for the Classic Electron Gas (Pxuiktsii
raspredeleniya dlya klassioheskogo elektronnogo gaza)
PERIODICAM Doklady Akademii Nauk.SSSR,19579VOl-114,Nr 6,pp.1210-1213(USSR)
ABSTRACTs According to the author's opinion various methods (mentioned
here)t in spite of their effectiveness in the calculation of
concrete problems, are not suitable for the removal of diffi-
culties in the construDtion of a radial function in systems
with pure Coulomb interaction. It was the object of the pre-
sent paper to improve the convergence of the development by
N. N. Bogolyubov for small intervals. First the system of
nonlinear integral equations obtained by Ns N. Bogolyubov
for Debyele expression G(r) for the radial function is written
down. In it the author replaces the unknown functions and
in this manner obtains the system -
If -4)(1q, I
V(J qJ )-(P(1 q 1)-~(J ql)+ dq q,
Card 1/3

Distribution Functions for the Classic Electron Gas
20-114-6-20/54
jq-q,j
dr d(~(r) . 8- ~(r)/Q C(r)j C(Iqj)- exp V(lq))J.
I dr
For the solution of this problem the author puts down
v For the determination
Rf V and C the serie2 developmenteare put down according to
exponents of vs
C(Iql)- co(lql)+v Cl(lql)+ v 2C2( jqj) . ........
V(Iql)- V 0(Iql)+v Vl(lql)+ v 2V2(jqj) . ........
Thu thus obtained equations of zeroth and first approximation
and the correction of first approximation are written down.
A Coulomb po:lntial with Debye soreeing is obtaineds
IP(I qj) . Tq-T e- Jq1/rd.
Then the solution of second approximatien equations is written
down. In disregard of second and higher approximation correc-
tions the following expression is obtained for the radial
Card 2/3 funotioni

20-114-6-20/54
Distribution Functions for the Classic Electron Gas
2 r/r
G(r) - exp 9 r d) This function can be obtained with-
out ternary approximation. The here discussed considerations
might, after several alter-ations, be applied to systems of
charged particles with different sign of charge. There are
2 references, 2 of which are Slavic.
ASSSOCIATIONs Mathematical Institute imeni V. A. Steklov of the AS USSR
(Matematicheskiy institut im. V. A. Steklova Akademii nauk
SSSR)
PRESENTEDs December 279 1957, by N. 11. Bogolyubov, Member of the Academy
SUBMITTEN December 14, 1956
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-- - TTABLIKGVv-kff-Vw; TOLMACHIV, Y.v.
Classical theory of strong electrolytes. Nauch. dokl. Tyu. skoly;
fizo-mat. nauki no.l-.101-109 '58. WRA 12:3)
l.Hatematicheskiy institut im. V.A. Staklova.
k1lectrolytes)

16(1)
AUTHORs SOV/155-56-5-31/37
TITLEt Generalized Variation Prinoiple'for the Several-Bodies
Problem
FERIODICALt Nauchnyye doklady vysshey shkoly. Fiziko-matematicheskiye
nauki,1958,Nr 5,PP 183-191 (USSR)
ABSTRACTs In Z_Ref 2-7 N.N. Bogolyubov formulates a generalized
variation principle for the several-bodies problem of quan-
tum mechanics by seeking the minimum of the functional
corresponding to the mean system energy on an extended class
of "vacuum" functions, In the present paper the author de-
rives the equations of this gene--,alized method and the con-
ditions for the stability of the solutions in a somewhat
modified form which is easier for the representation in co-
ordinates. - There are 5 rfferences, 4 of which are Soviet,
and I German.
A3SOCIATIONs Ylatematicheskiy institut Akademii nauk imeni V.A.Stekl
(Mathematical Institute,AS imeni V.A. Steklov)
SUBMITTE.Ds May 6; 1958 OV
Card 1/1

HUNGARY/Magnetism --Ferromagnetism. F
Abs Jour : Ref Zhur Fizi!:a, No 4, 1960, 8899
Author t Siklos Tivadar, Tyablikor SZ. V.
Inst
Title On the Quantum Theory of Ferromagnetic Anisotropy of
Uniaxial Crystals.
Orig Pub Magyar tud. akad. Kosp. fiz. Kutato int. Kozl., 1958,
6, No 5, 408-419
Abstract The anisotropy of magretic properties of ferromagnetic
crystals is considered as a result of anisotropic inter-
action between the electrons of the unfilled atomic
shells. The energy spectrun of the electrons of magne-
tic uniaxial ferromagnetic crystals are calculated as
functions of the saturation magnetization, measured in
directions parallel to an p,~rpezidicular to the princi-
pal axes of the crystal, on 'L-.he temperature, and on the
external magnetic field.
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TYA B k I K 6 V', --"S' , V i
AUTHORS: Tolmachev, V. V., Tyablikov, S. V. 56-i-i-j/.r6
TITLE: A New -~Lethod in the Theory of Superconductivit ii.
(Onovom, metode v teorii, sverkhprovodimooti. Il~:
PERIODICAL: Zhurnal Eksperimentalinoy i Teoreticheskoy Fizikig 1958,
Vol. 34, Nr 1, pp. 66-72 0133R)
ABSTRACT: The present paper shows the equivalence of the Hamlltonians
of the systems of Bardin and FrOblichs and thus estabglishes
the superconduotivity of the Bardin Namiltonian obtained in
this waj, For the calculations the 23o,*,-olyul)ov method is used.
It is a characteristic feature of the olectronphonou inter-
action discussed here that it is effective only In a very
thin layer on the Fermi levelg and considerably decreases
vrhen the distance from this level is increased. Therefore the
electron tranoitions on the Fermi level can es-sentially
contribute to all effectGo In this case the ennrgy of the
electron transitions may be regarded as small compared to the
energy t10 of the photions. Here a typical adiabatic
combination oocurn. At the beginning the Hamiltonian of th,~,
system investigated here is put doffn. Next the operator form
Card 1/3 of the perturbation theory is used. The determination of the

A Yew Method in the Theory of Superconductivity. 11, 56-1-11/56
eigenfunctions and eigenvalues is reduced to the oolution of
an equation with a certain "drformed" factor. Thic equation
is put down here in an explioli form with an exactness up
to the order of magnitude of P, inclusive. The authors here
investieate the case of the phonon vacuums The application
of the perturbation theory to the operator used here leads
to logarithmioal diver-enoes if the distance from the Fermi
level is inoreased. Then a canonical transformition is
exercised on the operators. The trivial aolutionof the aystem
of equation3 with corresponding oalculatloas oorros.-ponds to
the normal (not superconductine) state of the system. Then
asymptotic terms for the non-trivial solution ar6 given.
The energy of the elementary excitations Is calculated in the
first approximation with respeot to g2# Aftor that the
authors prove that the superconducting state is more
profitable as to energy than is the normal state. The formulae
received here are hardly susceptible to a change of the form
of the rociprooul aotioa.! assumed here. The ropulto dinounnel
as yet were received In the first perturbation theory
approximation. But the compensation of the diagrams of the
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A New Method in the Theory of Superconductivity. 11. 56-1-11/56
second degree (g 4) does not change the results.
There are 2 figures, and 5 references, 2 of which are
Slavic.
ASSOCIATION: Mathematical Institute of the AN USSR
(Matematichaskiy institut Akademii nauk SSSR).
SUBMITTED: October 17, 1957
AVAILIBLE: Library of Congress
Card 3/3

AUTHORS: Tyablikov, S. V., Tolirachev, V. V. 3011/56-34-5-29/61
TITLE: Electron Interaction With Lattice Vibrations
(0 vziiimodeystv.Ji elektronov s kolebaniyami reshetki)
PERIODICAL: Zhurnal eksperimentaltnoy i teoraticheskoy fizik-J, 195-51
Vol. 34, Nr j, pp. 11"A - 1257 (U-SER)
ABSTRACT: The authof-s inveoti.,rate the problem of the stability taking
into consideration the interaction of the electrons with the
phonoa f~'eld. 'The authors start frc-n the following
Hamiltonian 'o--- the interact-lon of the electrcn~with the
lattice vibrations
H = H + H H E(k)ak+,.ak6 + z1*10 1,I)b+b
0 int 0 k,d q a. q
H 60)1'k f -ka b
i nt k, k 1 6 % k+16'k6 kl-k+ ak6ak0k+'-k)
a + ak6, and b+, b respectively denote the creation- and
k6l k k
Card I annihilation o-verators of the electrons and the phonons re-

Electron Interaction With Lattice Vibrations 30'1/56-34-5-29/61
and F denotes the volume of the domain of the
main periodicity. The authors are interested in phonons with
sufficiently low energies, where t4)