Dependence on dilution of critical and compensation temperatures of a two-dimensional mixed spin-1/2 and spin-1 system

Aydıner, Ekrem; Yüksel, Yusuf; Kis-Cam, Ebru; Polat, Hamza

doi:10.1016/j.jmmm.2009.05.042

Cited by 14 publications

(4 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Furthermore, its applications also include the description of ternary fluids [15,16], solide-liquid-gas mixtures and binary fluids [17,18], microemulsions [19,20], ordering in semiconducting alloys [21,22] and electron conduction models [23]. Indeed, the BC model is found in many works using different lattices, spin degrees, including disorder and different Statistical Mechanic techniques [24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

A new effective correlation mean-field theory for the ferromagnetic spin-1 Blume–Capel model in a transverse crystal field

Viana

Salmon

Neto

et al. 2018

Int. J. Mod. Phys. B

View full text Add to dashboard Cite

A new approximating technique is developed so as to study the quantum ferromagnetic spin-1 Blume-Capel model in the presence of a transverse crystal field in the square lattice. Our proposal consists of approaching the spin system by considering islands of finite clusters whose frontiers are surrounded by non-interacting spins that are treated by the effective-field theory. The resulting phase diagram is qualitatively correct, in contrast to most effective-field treatments, in which the first-order line exhibits spurious behavior by not being perpendicular to the anisotropy axis at low temperatures. The effect of the transverse anisotropy is also verified by the presence of quantum phase transitions. The possibility of using larger sizes constitutes an advantage to other approaches where the implementation of larger sizes is costly computationally.PACS numbers: 64.60.Ak; 64.60.Fr; 68.35.Rh I. INTRODUCTIONIn general, many-body systems with interactions are very difficult to solve exactly. A way to overcome this difficulty is by approaching the many-body problem by a one-body problem, in which a mean-field replaces the interactions affecting the body. This idea is applied to the ferromagnetic Ising Model (see reference [1]). In the most simple mean-field approach, the nearest-neighbor interactions affecting each spin S i are replaced in such a way that S i now interacts with an effective field given by zJ S i , where z is the coordination number, J the exchange constant, and S i is the thermal average of the spin i. This is the so called "Weiss mean-field approach" [2]. Nevertheless, it neglects the spin correlations, and it leads the transition temperature T c as well as the values of the critical exponents away from the exact values (T c = zJ/k B , for all dimensions). However, for the one-dimensional case, the Ising model lacks of a phase transition at finite temperature, but Weiss' approach wrongly predicts that T c = 2J/k B . A further step for improving the solution of this problem, is to use the proposal of Hans Bethe, which consists in considering that a central spin should interact with all its nearest-neighbour spins forming a cluster [3]. Then, that cluster would interact to an effective field that approaches the next-nearest-neighbor spins surrounding the cluster. Thus, this improvement gives T c = 2J/k B ln(z/(z − 2)), which not only betters the approximation of the critical temperatures, but leads correctly to T c = 0, for the one-dimensional case. In this way, the correlations between the spins has been included to some degree by considering a cluster of spins interacting with its nearest-neighbors.A further step in approaching the many-body problem in spin systems is the effective-field approach. It is used in spin models with finite-size clusters based on the following Hamiltonian splitting:

show abstract

Section: Introductionmentioning

confidence: 99%

A new effective correlation mean-field theory for the ferromagnetic spin-1 Blume–Capel model in a transverse crystal field

Viana

Salmon

Neto

et al. 2018

Int. J. Mod. Phys. B

View full text Add to dashboard Cite

show abstract

“…solid-liquid-gas mixtures and binary fluids [17,18], micro-emulsions [19,20], ordering in semiconducting alloys [21,22] and electron conduction models [23]. Indeed, the BC model is found in many works using different lattices, spin degrees, including disorder and different Statistical Mechanic techniques [24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

A mean-field approach applied for the ferromagnetic spin-1 Blume-Capel model

Viana,

Salmon,

Neto

2016

Preprint

View full text Add to dashboard Cite

We applied a mean-field approach associated to Monte Carlo simulations in order to study the spin-1 ferromagnetic Blume-Capel model in the square and the linear lattice. This new technique, which we call MFT-MC, determines the molecular field as the magnetization response of a Monte Carlo simulation. The resulting phase diagram is qualitatively correct, in contrast to effectivefield approximations, in which the first-order line is not perpendicular to the anisotropy axis at low temperatures. Thermodynamic quantities, as the entropy and the specific heat curves can be obtained so as to analyze the nature of the phase transition points. Also, the possibility of using larger sizes constitutes an improvement regarding other mean-field approximations that use clusters.

show abstract

“…These systems have been studied extensively by using the well-known methods in equilibrium statistical physics. The well-known mixed spin Ising systems are (1/2, 1) [31,[41][42][43][44], (1/2, 3/2) [32,45,46], (1, 3/2) [47][48][49][50] and (2, 5/2) [51][52][53] Ising systems. Furthermore, the nonequilibrium aspects of mixed spins (1, 1/2) [54,55], (1/2, 3/2) [56,57], (1, 3/2) [58], (2, 5/2) [59], have been also investigated.…”

Section: Introductionmentioning

confidence: 99%

Hexagonal Type Ising Nanowire with Spin-1 Core and Spin-2 Shell Structure

Ertaş

Kantar

2015

Commun. Theor. Phys.

View full text Add to dashboard Cite

Thermodynamic properties and phase diagrams of a mixed spin-(1, 2) Ising ferrimagnetic system with single ion anisotropy on hexagonal nanowire are studied by using effective-field theory with correlations. The susceptibility, internal energy and specific heat of the system are numerically examined and some interesting phenomena in these quantities are found. The effect of the Hamiltonian parameters on phase diagrams are examined in detail. Besides second-order phase transition, lines of first-order transition and tricritical points are found. In particular, we found that for some negative values of single-ion anisotropies, there exist first-order phase transitions.

show abstract

Dependence on dilution of critical and compensation temperatures of a two-dimensional mixed spin-1/2 and spin-1 system

Cited by 14 publications

References 13 publications

A new effective correlation mean-field theory for the ferromagnetic spin-1 Blume–Capel model in a transverse crystal field

A new effective correlation mean-field theory for the ferromagnetic spin-1 Blume–Capel model in a transverse crystal field

A mean-field approach applied for the ferromagnetic spin-1 Blume-Capel model

Hexagonal Type Ising Nanowire with Spin-1 Core and Spin-2 Shell Structure

Contact Info

Product

Resources

About