Numerical study of the spin-3/2 Ashkin-Teller model
The study of the Ashkin-Teller model (ATM) of spin-3/2 on a hypercubic lattice is undertaken via Monte Carlo (MC) simulation. The phase diagrams are displayed and discussed in the physical parameter space. Rich physical properties are recovered, namely the second order transition and multicritical p...
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irk-123456789-1552602019-06-17T01:28:32Z Numerical study of the spin-3/2 Ashkin-Teller model Boudefla, R. Bekhechi, S. Hontinfinde, F. The study of the Ashkin-Teller model (ATM) of spin-3/2 on a hypercubic lattice is undertaken via Monte Carlo (MC) simulation. The phase diagrams are displayed and discussed in the physical parameter space. Rich physical properties are recovered, namely the second order transition and multicritical points. The phase diagrams have been obtained by varying the strength describing the four spin interaction and the single ion potential. This model shows a new high temperature partially ordered phase, called <S> and a new Baxter 3/2 ground state which do not exist neither in the spin-1/2 ATM nor in the spin-1 ATM. Вивчення моделi Ашкiна-Теллера спiн-3/2 на гiперкубiчнiй ґратцi здiйснюється методом Монте Карло. Продемонстровано фазовi дiаграми i обговорено простiр фiзичних параметрiв. Виявлено багатство фiзичних властивостей, а саме, перехiд другого роду i мультикритичнi точки. Фазовi дiаграми отриманi шляхом змiни сили, що описує чотириспiнову взаємодiю та одноiонний потенцiал. Дана модель демонструє нову високотемпературну частково впорядковану фазу, що називається 〈S〉, i новий основний 3/2 стан Бакстера, якого нема в моделях Ашкiна-Теллера спiн-1/2 i spin-1. 2015 Article Numerical study of the spin-3/2 Ashkin-Teller model / R. Boudefla, S. Bekhechi, F. Hontinfinde // Condensed Matter Physics. — 2015. — Т. 18, № 3. — С. 33703: 1–8. — Бібліогр.: 23 назв. — англ. 1607-324X PACS: 75.10.Hk DOI:10.5488/CMP.18.33703 arXiv:1510.06554 http://dspace.nbuv.gov.ua/handle/123456789/155260 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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The study of the Ashkin-Teller model (ATM) of spin-3/2 on a hypercubic lattice is undertaken via Monte Carlo (MC) simulation. The phase diagrams are displayed and discussed in the physical parameter space. Rich physical properties are recovered, namely the second order transition and multicritical points. The phase diagrams have been obtained by varying the strength describing the four spin interaction and the single ion potential. This model shows a new high temperature partially ordered phase, called <S> and a new Baxter 3/2 ground state which do not exist neither in the spin-1/2 ATM nor in the spin-1 ATM. |
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Boudefla, R. Bekhechi, S. Hontinfinde, F. |
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Boudefla, R. Bekhechi, S. Hontinfinde, F. Numerical study of the spin-3/2 Ashkin-Teller model Condensed Matter Physics |
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Boudefla, R. Bekhechi, S. Hontinfinde, F. |
| author_sort |
Boudefla, R. |
| title |
Numerical study of the spin-3/2 Ashkin-Teller model |
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Numerical study of the spin-3/2 Ashkin-Teller model |
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Numerical study of the spin-3/2 Ashkin-Teller model |
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Numerical study of the spin-3/2 Ashkin-Teller model |
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Numerical study of the spin-3/2 Ashkin-Teller model |
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numerical study of the spin-3/2 ashkin-teller model |
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Інститут фізики конденсованих систем НАН України |
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Numerical study of the spin-3/2 Ashkin-Teller model / R. Boudefla, S. Bekhechi, F. Hontinfinde // Condensed Matter Physics. — 2015. — Т. 18, № 3. — С. 33703: 1–8. — Бібліогр.: 23 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT boudeflar numericalstudyofthespin32ashkintellermodel AT bekhechis numericalstudyofthespin32ashkintellermodel AT hontinfindef numericalstudyofthespin32ashkintellermodel |
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2025-07-14T07:19:14Z |
| last_indexed |
2025-07-14T07:19:14Z |
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1837606626403549184 |
| fulltext |
Condensed Matter Physics, 2015, Vol. 18, No 3, 33703: 1–8
DOI: 10.5488/CMP.18.33703
http://www.icmp.lviv.ua/journal
Numerical study of the spin-3/2 Ashkin-Teller model
R. Boudefla1∗, S. Bekhechi1, F. Hontinfinde2
1 Laboratoire de Physique Thtéorique (LPT), B.P. 230, Université Abou Bekr Belkaïd, Tlemcen 13000, Algeria
2 Département de Physique (FAST) et Institut des Mathématiques et de Sciences Physiques (IMSP), Université
d’Abomey-Calavy, 01 B.P. 613, Porto-Novo, Benin
Received November 8, 2014, in final form May 10, 2015
The study of the Ashkin-Teller model (ATM) of spin-3/2 on a hypercubic lattice is undertaken via Monte Carlo
simulation. The phase diagrams are displayed and discussed in the physical parameter space. Rich physical
properties are recovered, namely the second order transition and multicritical points. The phase diagrams have
been obtained by varying the strength describing the four spin interaction and the single ion potential. This
model shows a new high temperature partially ordered phase, called 〈S〉 and a new Baxter 3/2 ground state
which do not exist either in the spin-1/2 ATM or in the spin-1 ATM.
Key words: modelization, Ashkin-Teller, spin-3/2, Monte-Carlo, phase diagram, Baxter
PACS: 75.10.Hk
1. Introduction
In this work, we will analyze a magnetic model with three spin states known as Ashkin-Teller model
[1] which is a superposition of two Ising models with spin variables σ and S. In every site i of the cubic
lattice, two spin variables σi and Si are associated. In each Ising model, there are two spin nearest-
neighbors interactionwith a strength K2 [2]. In addition, different Isingmodels are coupled by a four-spin
interaction with strength K4 [3] and on each site there is a single ion potentialD [2]. All these interactions
are limited to the first nearest neighbors.
Recent researches of this Ising model and its phase diagrams with four spin interaction and some of
its applications have been done [4–8].
The selenium compound adsorbed on a nickel surface [9] is a good physical picture for this model.
Different methods have been used to understand the critical behaviour of this model. For the two dimen-
sional case, all of mean-field approximation (MFA) [10–13] Monte Carlo simulations (MC) [11–14], series
analysis [15], exact duality [16], transfer-matrix finite size scaling calculations [9, 14, 17], renormaliza-
tion group [18, 19] and mean field renormalization group approach [20], yield three different phases: a
paramagnetic phase in which neither σ nor S nor anything else is ordered (〈σ〉 = 〈S〉 = 〈σS〉 = 0); Baxter
phase in which σ and S independently order in ferromagnetic fashion, and also 〈σS〉 , 0; a third phase
called PO1 in which σS is ferromagnetically ordered 〈σS〉, 0 but 〈σ〉 = 〈S〉 = 0.
One of the most interesting and challenging phenomena is the appearance of other new partially
ordered phases in the ATM. For example, MFA and MC simulations applied to the three-dimensional case
yield first and second-order phase transitions and partially ferromagnetic ordered phase 〈σ〉 (〈σ〉, 0 and
〈S〉 = 〈σS〉 = 0) [11]. By using exact duality transformations and symmetry considerations [17, 21], the
anisotropic ATM in d = 2 also presents partially ordered phases called 〈σ〉 and 〈S〉 which are connected
by symmetry operations to the 〈σS〉 phase. These results are confirmed in d = 2 and d = 3 by MFA and
MC simulations [12]. The PO2 phase defined by (〈S〉 = 〈σ〉, 0; 〈σS〉 = 0) found in the spin-1 Ashkin-Teller
model [14, 22] does not occur in the spin-1/2 Ashkin-Teller model [12].
∗raniaboudefla@yahoo.com
© R. Boudefla, S. Bekhechi, F. Hontinfinde, 2015 33703-1
http://dx.doi.org/10.5488/CMP.18.33703
http://www.icmp.lviv.ua/journal
R. Boudefla, S. Bekhechi, F. Hontinfinde
Monte Carlo (MC) simulation can be shown as a powerful and successful tool to study critical phenom-
ena [12] at reduced dimensionality (d = 2). So, it is of importance to fully understand the phase diagram
obtained from this model through a nonperturbative method, such as Monte Carlo technique. The main
problem which arises from this method is the existence of statistical errors.
In this paper, wemainly focused on the spin-3/2 Ashkin-Teller model usingMC simulations. The paper
is organized as follows: in the second section, the investigated model is introduced and the ground state
diagram is presented. Section 3 contains the description of the methodology and formalism of the MC
simulations. We collect our results and discussions in section 4. Finally, the summary and conclusions
are drawn in section 5.
2. Model and ground state diagram
The Hamiltonian of the model can be expressed as:
H =−K2
∑
〈i j 〉
(
σiσ j +Si S j
)
−K4
∑
〈i j 〉
σiσ j Si S j −D
∑
〈i〉
(
S2
i +σ
2
i
)
, (2.1)
where the spins σi and Si are located on sites of an hypercubic lattice and take both the values ±3/2
and ±1/2. The first term describes the bilinear interactions between the spins at sites i and j , with the
interaction parameter K2. The second term describes the four-spins interaction with strength K4 and on
each site there is a single ion potential D. All these interactions are restricted to the z nearest neighbours
pairs of spins.
In order to calculate the ground state energy, we express the hamiltonian as a sum of contributions
of the nearest-neighbour spins. So, the contribution of a pair S1, S2 and σ1, σ2 is:
Ep =−K2(σ1σ2 +S1S2)−K4σ1σ2S1S2 −D
(
S2
1 +S2
2 +σ
2
1 +σ
2
2
)
. (2.2)
By comparing the values of Ep for different configurations, we obtain the following structure of phase
diagram shown in figure 1:
(i) For K4/K2 < D/K2: if K4/K2 < −0.4, the spins σi are parallel while the spins Si are antiparallel.
Then we have: 〈S〉F = 〈σ〉AF = 〈σS〉F = 0 and 〈S〉AF = 〈σ〉F = 3/2 and 〈σS〉AF , 0 which characterize
the phase called Baxter-3/2, otherwise if K4/K2 > −0.4 the Baxter-3/2 phase is stable since both
spins σi and Si are aligned and equal to 3/2.
(ii) For K4/K2 > D/K2: if K4/K2 < −4, the spins σi are parallel while the spins Si are antiparallel.
Then we have: 〈S〉F = 〈σ〉AF = 〈σS〉F = 0 and 〈S〉AF = 〈σ〉F = 1/2 and 〈σS〉AF , 0 which characterize
the phase called Baxter-1/2. The symbols 〈. . .〉F and 〈. . .〉AF indicate the thermal average of spin
variables respectively in the ferromagnetic and antiferromagnetic phases, or else if K4/K2 > −4,
the Baxter-1/2 phase is stable since both spins σi and Si are aligned and equal to 1/2.
(iii) Except for K4/K2 > D/K2, in the area 0 < D/K2 < −1, two Baxter mixed phases have been found,
the first when K4/K2 >−0.4, all the spinsσi and Si are parallel, and the second one ifK4/K2 <−0.4,
the spins Si are parallel while the spins σi are misaligned.
3. Monte-carlo simulations
The system studied here is a L ×L square lattice with even values of L, containing N = L2 spins. In
order to update the lattice configurations, the well-known Metropolis algorithm [12] is used with periodic
boundary conditions. Monte-Carlo (MC) simulations are performed for d = 2with systems of sizes L = 10,
16, 20, 30, 40 and 60. We use 100000 to 200000 MC steps to calculate the thermodynamic quantities after
discarding 5000–50000 sweeps for thermal equilibrium. Most of the phase diagrams presented here are
33703-2
Numerical study of the spin-3/2 Ashkin-Teller model
D/K2
0-1
-1
-8
1
-1
-2
-3
-4
-5
-6
-7
0
2
8
7
6
5
4
3
-10 -9 -8 -7 -6 -5 -4 -3 -2 0 1 2 3 4 5 6 7 8
K
/K
4
2
Baxter
1/2
Baxter
3/2
Baxter
-1/2
Baxter
-3/2
Figure 1. Ground state phase diagram.
obtained with L = 30. The physical quantities of use are the magnetizations |Mα|(α = σ,S,σS), and are
estimated by:
|Mα| = 〈|Mα|〉 =
1
N p
∑
c
∑
i
αi (c) with α=σ,S,σS, (3.1)
where i runs over the lattice sites, c runs over the configurations obtained to update the lattice over
one sweep of the N spins of the lattice [one Monte-Carlo step (MCS)] counted after the system reaches
thermal equilibrium, and p is the number of the MCS. In order to measure the phase boundaries, we
find useful the measurement of fluctuations (variance of the order-parameters) in Mα defined by the
magnetic susceptibility:
χα =
N
kBT
(
〈M2
α〉−〈| Mα |〉
2
)
with α=σ,S,σS, (3.2)
kB is the Boltzmann’s constant.
4. Results and discussion
The phase diagram obtained by Monte Carlo simulation is shown in figure 2 and presented in the
plane (kBT /K2,D/K2). We have a paramagnetic phase, where 〈σ〉 = 〈S〉 = 〈σS〉 = 0 and two ferromagnetic
(Baxter) phases, where 〈σ〉 and 〈S〉 are ordered ferromagnetically and also 〈σS〉, 0. The first is Baxter-1/2
and the second is the Baxter-3/2which were not found in the earlier works [13, 14]. These phases are sepa-
rated by critical lines, multicritical points and two partially ordered phases: the 〈σS〉 phase where (〈σS〉,
0 and 〈σ〉 = 〈S〉 = 0) and the 〈S〉 phase where (〈σ〉 = 〈σS〉 = 0, 〈S〉, 0). However, the MC data are obtained
from peaks in the susceptibilities [23] for L = 30. The nature of the transition is determined from disconti-
nuities (continuities) in the order parameters for first (second) order transition byMC simulations [12]. In
our paper, the nature of the transitions is always of second order for all values. We have located the phase
boundaries by using the maximum of the susceptibility. This method has been successfully applied to
othermodels [13] and has shown a good precisionwith the transfer matrix finite-size-scaling method [14].
The results of figure 2 are obtained for K4 = 0.25. We also see the Baxter-1/2 phase separated from the
paramagnetic phase by the partially ordered phase 〈σS〉 at low values of D/K2, as seen in the figures 3, 4
and the Baxter-3/2 phase is separated from the paramagnetic phase by the new partially ordered phase
33703-3
R. Boudefla, S. Bekhechi, F. Hontinfinde
Figure 2. Phase diagram in the (D/K2,T /K2) plane for K4 = 0.25 from Monte Carlo simulation, data are
shown with L = 30.
〈S〉 at high values of D/K2, as seen in the figures 5, 6. This phase does not exist either in the spin-1/2 [12]
or in the spin-1 [14] Ashkin-Teller model but is viewed in the mixed (ATM) [13]. The meeting of all critical
lines is located at the multicritical points A(−2.98±0.01;0.77±0.01) and B(−2.54±0.01;3.97±0.01). The
two phases 〈σS〉 and 〈S〉 separate the disordered phase from the ferromagnetic Baxter phases by second
order transition lines.
For error bars, we have made 300000 MCS and discarding 50000 and made measurements every 100
MCS, we plotted errors to the magnetizations and susceptibilities, as seen in the figures 3–6 which present
plot of the three order-parameters σ, S and σS as function of temperature for K4 = 0.25 and D =−5 (and
D = 15) as obtained byMC simulations showing that the error bars are very small, the simulation was too
long, it took a lot of computing time.
By increasing the four body interaction, K4/K2, the two Baxter phases remain in the phase diagrams
whereas depending on the strength of K4, as shown in figure 7 for K4 = 2, the partially ordered phase
〈σS〉 shrinks and the other one 〈S〉 disappears. But for strong K4, K4 = 6, the partially ordered phase
〈σS〉 disappears and the other partially phase 〈S〉 is recovered as shown in figure 8. Continuous lines are
Figure 3. Plot of the three order-parameters 〈σS〉, 〈σ〉 and 〈S〉with error bars as function of temperature
for K4 = 0.25 and D = −5 as obtained by MC simulations for the square lattice showing that the phase
transitions are of second-order.
33703-4
Numerical study of the spin-3/2 Ashkin-Teller model
Figure 4. Plot of the susceptibility with error bars for K4 = 0.25 and D =−5 as functions of temperature
showing the existence of the phase 〈σS〉, where at T ′
1
= 1.20, 〈σS〉 , 0 and 〈σ〉 = 〈S〉 = 0, whereas at
T ′′
1
= 6.48 we have 〈σ〉 = 〈S〉 = 〈σS〉= 0.
linked by multicritical points of higher order.
5. Conclusion
In this paper, by using MC simulations we have shown that the isotropic ferromagnetic Ashkin-Teller
model presents a new partially ordered phase 〈S〉, which is very clear at high temperatures (also found
infinitesimal in the Monte Carlo mixed ATM [13]), and other phases like Baxter-3/2 where all spins have
the magnitude of 3/2. In the parameter space (K4/K2, D/K2 and T /K2), the phase diagrams present rich
varieties of phase transitions with surfaces of second order phase transitions, bounded by lines of multi-
critical points.
In conclusion, the study was carried out on the model of Ashkin-Teller spin-3/2. It has revealed the
complexity of the model with very rich structures and gives a better understanding of the properties
Figure 5. Plot of the three order-parameters 〈σS〉, 〈σ〉 and 〈S〉with error bars as function of temperature
for K4 = 0.25 and D = 15 as obtained by MC simulations for the square lattice showing that the phase
transitions are of second-order.
33703-5
R. Boudefla, S. Bekhechi, F. Hontinfinde
Figure 6. Plot of the susceptibility with error bars for K4 = 0.25 and D = 15 as functions of temperature
showing the existence of the phase 〈S〉, where at T ′
2
= 11.10, 〈σ〉 = 〈σS〉= 0, 〈S〉, 0, whereas at T ′′
2
= 14.21
we have 〈σ〉 = 〈S〉= 〈σS〉= 0.
of condensed matter, especially magnetic properties of the systems consisting of many atom molecules
holders. It is on the basis of this study that we plan to study the magnetic properties of the Ashkin-Teller
model with mixed spins on different types of lattices. The presence of many atoms with different mag-
netic moments on the same site can reveal some interesting properties. The model will also be analyzed
in three dimensions including the crystal fields and long range interactions.
References
1. Ashkin J., Teller E., Phys. Rev., 1943, 64, 178; doi:10.1103/PhysRev.64.178.
2. Kogut J.B., Rev. Mod. Phys., 1979, 51, 659; doi:10.1103/RevModPhys.51.659.
3. Barreto F.C.S., Braz. J. Phys., 2013, 41, 43; doi:10.1007/s13538-012-0104-z.
4. Chatelain C., Condens. Matter Phys., 2011, 17, 33601; doi:10.5488/CMP.17.33601.
5. Huang Y., Deng Y., Jacobsen J.L., Salas J., Nucl. Phys. B, 2013, 868, 492; doi:10.1016/j.nuclphysb.2012.11.015.
6. Chang Z., Wang P., Zheng Y.-H., Commun. Theor. Phys., 2008, 49, 525; doi:10.1088/0253-6102/49/2/57.
Figure 7. Phase diagram in the (D/K2,T /K2) plane for K4 = 2 from Monte Carlo simulation, data are
shown with L = 30.
33703-6
http://dx.doi.org/10.1103/PhysRev.64.178
http://dx.doi.org/10.1103/RevModPhys.51.659
http://dx.doi.org/10.1007/s13538-012-0104-z
http://dx.doi.org/10.5488/CMP.17.33601
http://dx.doi.org/10.1016/j.nuclphysb.2012.11.015
http://dx.doi.org/10.1088/0253-6102/49/2/57
Numerical study of the spin-3/2 Ashkin-Teller model
Figure 8. Phase diagram in the (D/K2,T /K2) plane for K4 = 6 from Monte Carlo simulation, data are
shown with L = 30.
7. Le J.-X., Yang Zh.-R., Commun. Theor. Phys., 2005, 43, 841; doi:10.1088/0253-6102/43/5/017.
8. Bezerraa C.G., Mariza A.M., de Araújo J.M., da Costaa F.A., Physica A, 2001, 292, 429;
doi:10.1016/S0378-4371(00)00568-9.
9. Bak P., Kleban P., Unertel W.N., Ochab J., Akinci G., Barlet N.C., Einstein T.L., Phys. Rev. Lett., 1985, 54, 1542;
doi:10.1103/PhysRevLett.54.1539.
10. Zhang G.M., Yang C.Z., Phys. Rev. B, 1993, 48, 9452; doi:10.1103/PhysRevB.48.9452.
11. Ditzian R.V., Banavar J.R., Grest G.S., Kadano L.P., Phys. Rev. B, 1980, 22, 2542; doi:10.1103/PhysRevB.22.2542.
12. Bekhechi S., Benyoussef A., Elkenz A., Ettaki B., Loulidi M., Physica A, 1999, 264, 503;
doi:10.1016/S0378-4371(98)00474-9.
13. Bekhechi S., Benyoussef A., Elkenz A., Ettaki B., Loulidi M., Eur. Phys. J. B, 2000, 18, 278;
doi:10.1007/s100510070058.
14. Badehdah M., Bekhechi S., Benyoussef A., Ettaki B., Phys. Rev. B, 1999, 59, 6250; doi:10.1103/PhysRevB.59.6250.
15. Ditzian R.V., Phys. Lett. A, 1972, 38, 451; doi:10.1016/0375-9601(72)90032-1.
16. Wegner F.J., J. Phys. C: Solid State Phys., 1972, 5, L131; doi:10.1088/0022-3719/5/11/004.
17. Badehdah M., Bekhechi S., Benyoussef A., Touzani M., Physica B, 2000, 291, 394;
doi:10.1016/S0921-4526(00)00279-9.
18. Banavar J.R., Jasnow D., Landau D.P., Phys. Rev. B, 1979, 20, 3820; doi:10.1103/PhysRevB.20.3820.
19. Knops H.J.F., J. Phys. A: Math. Gen., 1975, 8, 1508; doi:10.1088/0305-4470/8/9/020.
20. Plascak J.A., Sa Barreto F.C., J. Phys. A: Math. Gen., 1986, 19, 2195; doi:10.1088/0305-4470/19/11/027.
21. Wu F.Y., Lin K.Y., J. Phys. C: Solid State Phys., 1974, 7, L181; doi:10.1088/0022-3719/7/9/002.
22. Loulidi M., Phys. Rev. B, 1997, 55, 11611; doi:10.1103/PhysRevB.55.11611.
23. Ditzian R.V., J. Phys. C: Solid State Phys., 1972, 5, L250; doi:10.1088/0022-3719/5/17/005.
33703-7
http://dx.doi.org/10.1088/0253-6102/43/5/017
http://dx.doi.org/10.1016/S0378-4371(00)00568-9
http://dx.doi.org/10.1103/PhysRevLett.54.1539
http://dx.doi.org/10.1103/PhysRevB.48.9452
http://dx.doi.org/10.1103/PhysRevB.22.2542
http://dx.doi.org/10.1016/S0378-4371(98)00474-9
http://dx.doi.org/10.1007/s100510070058
http://dx.doi.org/10.1103/PhysRevB.59.6250
http://dx.doi.org/10.1016/0375-9601(72)90032-1
http://dx.doi.org/10.1088/0022-3719/5/11/004
http://dx.doi.org/10.1016/S0921-4526(00)00279-9
http://dx.doi.org/10.1103/PhysRevB.20.3820
http://dx.doi.org/10.1088/0305-4470/8/9/020
http://dx.doi.org/10.1088/0305-4470/19/11/027
http://dx.doi.org/10.1088/0022-3719/7/9/002
http://dx.doi.org/10.1103/PhysRevB.55.11611
http://dx.doi.org/10.1088/0022-3719/5/17/005
R. Boudefla, S. Bekhechi, F. Hontinfinde
Чисельне вивчення спiн-3/2 моделi Ашкiна-Теллера
Р. Будефля1, С. Бекешi1, Ф. Гонтiнфiнде2
1 Лабораторiя теоретичної фiзики, B.P. 230, Унiверситет Абу Бакр Белькаїд, Тлемсен 13000, Алжир
2 Вiддiлення фiзики (FAST) та iнститут математики i фiзичних наук (IMSP), Унiверситет Абомей-Калавi, Бенiн
Вивчення моделi Ашкiна-Теллера спiн-3/2 на гiперкубiчнiй ґратцi здiйснюється методом Монте Карло.
Продемонстровано фазовi дiаграми i обговорено простiр фiзичних параметрiв. Виявлено багатство фi-
зичних властивостей, а саме, перехiд другого роду i мультикритичнi точки. Фазовi дiаграми отриманi
шляхом змiни сили, що описує чотириспiнову взаємодiю та одноiонний потенцiал. Дана модель демон-
струє нову високотемпературну частково впорядковану фазу, що називається 〈S〉, i новий основний 3/2
стан Бакстера, якого нема в моделях Ашкiна-Теллера спiн-1/2 i spin-1.
Ключовi слова: моделювання, Ашкiн-Теллер, спiн-3/2, Монте-Карло, фазова дiаграма, Бакстер
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Introduction
Model and ground state diagram
Monte-carlo simulations
Results and discussion
Conclusion
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