Real-space renormalization group investigation of pure and disordered mixed spin Ising models ond-dimensional lattices

Benayad, N.

doi:10.1007/bf01454220

Cited by 46 publications

(14 citation statements)

References 21 publications

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“…C I C Also, the results shown in figure 6 for S=3/2 are in complete agreement with the Monte Carlo studies [15]. On the other hand, we confirm that there is no tricritical point for any value of Δ and any integer value of S. In particular, we have to mention that our exact calculations confirm the result obtained previously in the case of spin S=1 by Monte Carlo simulations [16][17][18] and, as one of us (N. Benayad) has predicted using renormalization-group method [19]. These results are depicted in figure 7.…”

Section: Resultssupporting

confidence: 91%

“…We showed that, in both cases (S integer and half-odd-integer), the current system exhibits only second order transition without tricritical behavior as suggested previously by approximated methods EFT [20] and FCA [21,22]. On the other hand, our exact results confirm those obtained using Monte Carlo simulations [16][17][18] and renormalization group method [19] did for S=1. This is also the case for S=2 [23] and S=3/2 [15] using Monte Carlo simulations.…”

Section: Discussionsupporting

confidence: 89%

“…Figure 7. Comparison between our results and those in [16] and [19]. The solid line expresses our exact solution of the present system (S=1).…”

Section: Discussionmentioning

confidence: 65%

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Exact phase diagram for the mixed spin-1/2 and spin-S Ising models on the square lattice

2018

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We propose a new approach which permits us to obtain exact results for the mixed spin-1/2 and Spin-S (S>1/2) Ising models with single ion anisotropy Δ on the square lattice. We drive an explicit expression for the critical temperature for arbitrary values of S. We determine the exact phase diagrams for different values of S, and we show that there is no tricritical point. For S integer, there is no long range order when the anisotropy exceeds a critical value which is independent of S. Furthermore, the exact Ising transition temperature T C is always recovered, for any values of S, in the limit of Δ→−∞. These exact results are based on a conjecture which extend the analyticity of the n-spin-1/2 correlations functions (except at T=T C (Ising)) for any finite number n, to n→∞. This is confirmed by our calculations since our results are practically similar to those obtained by Monte Carlo simulations for S=1, 2 and 3/2.

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Section: Resultssupporting

confidence: 91%

Section: Discussionsupporting

confidence: 89%

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Exact phase diagram for the mixed spin-1/2 and spin-S Ising models on the square lattice

2018

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“…Then, for any values of p A Y p B and D, one can find that the condition of (23) is always satisfied for the system with s 3 2 and hence the phase transition is also of second order. On the other hand, the compensation temperature can be determined by introducing the condition m B Àm A into the coupled equations (2), (3), (11) and (12). Fig.…”

Section: The Mixed-spin System With S 3mentioning

confidence: 99%

Magnetic Properties of Diluted Mixed Spin-� and Spin-s Ising Ferrimagnets with a Crystal Field

Bobák

Horváth

1999

phys. stat. sol. (b)

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The magnetic properties (transition temperature, compensation temperature and magnetization curve) of diluted mixed spin‐½ and spin‐s (s = 1; ⅔ Ising ferrimagnets with crystal field interaction D on a simple cubic lattice (z = 6) are investigated within the framework of the effective‐field theory with correlations. We find some characteristic behaviors of the magnetic properties, such as the possibility of many compensation points induced by the dilution and crystal field. The tricritical points in the system with s = 1 are also discussed.

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“…The existence of tricritical behaviour is still controversial. Effective field theory with correlations (EFT) [5] and finite cluster approximation [6] predict tricritical behaviour in systems with a coordination number z larger than 3 while renormalization group studies [7] for any dimension d and Monte Car10 calculations [8] for z = 4 give a second order phase transition for all values of the crystal field interaction. It is important to note here that the exact solution for the transition temperature, which is always of second order, can be obtained analytically if the structure of the system is chosen to be a honeycomb lattice (z = 3) [9, 101.…”

Section: Introductionmentioning

confidence: 99%

Mixed spin‐ and spin‐ Ising models with random nearest‐neighbour interactions

Benayad¹,

Dakhama²,

Klümper

et al. 1996

Annalen der Physik

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Using the effective field theory with correlations, we study mixed spin4 and spin-: Ising models with random bonds and crystal-field interactions on the honeycomb lattice. The nearestneighbour couplings J,, are taken as random variables with distribution P(J,j) = p6(Ji, -J)+(1 -p)6(Jiid), where J > 0 and (a( 5 1. In a certain range of negative values of a, the phase diagrams exhibit re-entrant behaviour. In detail, we investigate separately two kinds of disorder:bond dilution (a = 0) and random fJ interactions (a = -1). In both cases, the influence of the anisotropy on the phase diagrams shows some new outstanding features.

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Real-space renormalization group investigation of pure and disordered mixed spin Ising models ond-dimensional lattices

Cited by 46 publications

References 21 publications

Exact phase diagram for the mixed spin-1/2 and spin-S Ising models on the square lattice

Exact phase diagram for the mixed spin-1/2 and spin-S Ising models on the square lattice

Magnetic Properties of Diluted Mixed Spin-� and Spin-s Ising Ferrimagnets with a Crystal Field

Mixed spin‐ and spin‐ Ising models with random nearest‐neighbour interactions

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