Phase Diagrams of a Spin‐One Ising Model with a Random Crystal Field in the Correlated Effective‐Field Treatment

A spin-1 Blume-Capel model with dilute and random crystal fields is examined for honeycomb and square lattices by introducing an effective-field approximation that takes into account the correlations between different spins that emerge when expanding the identities. For dilute crystal fields, we have given a detailed exploration of the global phase diagrams of the system in kBTc/J − D/J plane with the second and first order transitions, as well as tricritical points. We have also investigated the effect of the random crystal field distribution characterized by two crystal field parameters D/J and △/J on the phase diagrams of the system. The system exhibits clear distinctions in qualitative manner with coordination number q for random crystal fields with △/J, D/J = 0. We have also found that, under certain conditions, the system may exhibit a number of interesting and unusual phenomena, such as reentrant behavior of first and second order, as well as a double reentrance with three successive phase transitions.

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“…where γ = (q − 1)A with q = 4, and the functions F (x) and G(x) are defined in equations (9) and (17).…”

Section: Discussionmentioning

confidence: 99%

“…Critical concentration p * obtained by several methods and the present work for honeycomb (q = 3) and square (q = 4) lattices.Lattice EFT-I8,9 EFT-II 10 MFT 13,15 PA 20 Present Work…”

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confidence: 96%

Critical behavior and phase diagrams of a spin-1 Blume–Capel model with random crystal field interactions: An effective field theory analysis

Yüksel

Akıncı

Polat

2012

Physica A: Statistical Mechanics and its Applications

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“…(17) and (18) and using the coefficients given by Eqs. (19) and (20) we get EFT results for the spin-S BC model. Linearization of Eqs.…”

Section: Model and Formulationmentioning

confidence: 99%

“…1 (a), (c), (e) for integer S and (b), (d), (f) for half integer S. Indeed these diagrams have already been obtained for specific values of S in the literature with several methods. For instance, for S − 1, 3/2, 2 within the PA [34], S − 1 within MC [5], FCA [9], MFA [12][13][14][15] and EFT [18][19][20], S − 3/2 model with crystal field dilution EFT [30], S − 2 EFT [33]. As seen in Fig.…”

Section: Phase Diagramsmentioning

confidence: 99%

“…The phase diagrams and thermodynamical properties of the S-1 BC model has been widely studied with several methods, such as the renormalization group (RG) technique [4], Monte Carlo (MC) simulations [5], cluster variational method (CVM) [6,7], finite cluster approximation (FCA) [8,9], pair approximation (PA) [10], replica method [11], mean field approximation (MFA) [12][13][14][15][16][17] and effective field theory (EFT) [18][19][20][21][22][23]. Besides, some other geometries have been investigated, such as Bethe lattice [24], thin film [25,26], nanowire [27], semi infinite geometry [28].…”

Section: Introductionmentioning

confidence: 99%

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Hysteresis behaviors of the crystal field diluted general spin-S Ising model

Akıncı

2017

Physics Letters A

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Hysteresis characteristics of the crystal field diluted general Spin-S (S > 1) Blume-Capel model have been studied within the effective field approximation. Particular emphasis has been paid on the large negative valued crystal field and low temperature region and it has been demonstrated for this region that, rising dilution of the crystal field results in decreasing number of windowed hysteresis loops. The evolution of the multiple hysteresis loop with the dilution of the crystal field has been investigated and physical mechanism behind this evolution has been given.

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Phase Diagrams of the Spin‐1 Blume‐Capel Model with a Random Crystal Field in the Cluster Expansion Theory

Ilkovič

1995

Physica Status Solidi (b)

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The phase diagram of the spin-1 Blume-Cape1 model in a random crystal field di obeying a two-valued distribution P(di) = p 6(di -d) + (1 -p ) 6(di) has been studied by the two-spin cluster expansion. In a previous investigation [l, 21 the phase diagram of this model with a random crystal field has been obtained within the mean-field approximation (MFA). In this note we study, via a two-spin cluster in the cluster expansion theory (CE) originally due to Strieb et al. [3], the influence of crystal-field disorder on the (d, T ) phase diagram at a given concentration p .The reduced (divided by p-' = kT) Hamiltonian of the system is given by where K = p J > 0, Sf = 0, + 1, J is the exchange parameter, and h is the external magnetic field. The first summation is over all nearest-neighbor pairs and the second summation is over all the lattice sites. The phase diagram of this model is determined by calculating the contributions to the free energy up to two-spin cluster in the CE theory. The average free energy per site is given byS is the internal-field parameter which describes the long-range order and whose best value is determined by minimizing the free energy.') Moyzesova 16, 04001 KoSice, Slovak Republic.

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Phase Diagrams of a Spin‐One Ising Model with a Random Crystal Field in the Correlated Effective‐Field Treatment

Abstract: The phase diagram of the spin-one Ising model with a random crystal field D, on a square lattice is investigated by the use of the correlated effective-field theory, when the random crystal field is distributed

Cited by 22 publications

References 11 publications

Critical behavior and phase diagrams of a spin-1 Blume–Capel model with random crystal field interactions: An effective field theory analysis

Critical behavior and phase diagrams of a spin-1 Blume–Capel model with random crystal field interactions: An effective field theory analysis

Hysteresis behaviors of the crystal field diluted general spin-S Ising model

Phase Diagrams of the Spin‐1 Blume‐Capel Model with a Random Crystal Field in the Cluster Expansion Theory

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