The spin-1 Ising model with a random crystal field: the mean-field solution

Benyoussef, A.; Biaz, T.; Saber, M.; Touzani, M.

doi:10.1088/0022-3719/20/32/021

Cited by 64 publications

(39 citation statements)

References 5 publications

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“…For weak disorder(p < 0.046 and p > 0.954), the phase diagram is similar to the pure Blume Capel model. In constrast to earlier studies [16,21], we find that the line of first order transitions end at a finite ∆ at zero temperature.…”

Section: Introductionsupporting

confidence: 78%

“…For example, the solution obtained using pair approximation [19] does not have the symmetry around p. Similarly, other approximations [16,21], predict a finite transition temperature for all non zero strengths of disorder, which has been proven incorrect by earlier studies using effective field theory [22]. This is because, these treatments deal with only one order parameter (m) and the entropy of zero spin state is not fully accounted for in these approximations.…”

Section: Discussionmentioning

confidence: 99%

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Absence of first order transition in the random crystal field Blume–Capel model on a fully connected graph

Sumedha¹,

Jana²

2016

J. Phys. A: Math. Theor.

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In this paper we solve the Blume-Capel model on a complete graph in the presence of random crystal field with a distribution, P (∆ i ) = pδ(∆ i − ∆) + (1 − p)δ(∆ i + ∆), using large deviation techniques. We find that the first order transition of the pure system is destroyed for 0.046 < p < 0.954 for all values of the crystal field, ∆. The system has a line of continuous transition for this range of p from −∞ < ∆ < ∞. For values of p outside this interval, the phase diagram of the system is similar to the pure model, with a tricritical point separating the line of first order and continuous transitions. We find that in this regime, the order vanishes for large ∆ for p < 0.046(and for large −∆ for p > 0.954) even at zero temperature.

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Section: Introductionsupporting

confidence: 78%

Section: Discussionmentioning

confidence: 99%

Absence of first order transition in the random crystal field Blume–Capel model on a fully connected graph

Sumedha¹,

Jana²

2016

J. Phys. A: Math. Theor.

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“…In particular, the spin-one Ising model with a random crystal-field interaction should be referred here, since some outstanding results may be obtained in going from the MFA to more sophisticated theories [40]. The Hamiltonian of the model is defined, instead of the BC model (86), by where Di is a random crystal-field constant distributed according to a probability distribution function P(Di), such as Within the framework of the MFA, several authors have examined the phase diagram of the model and predicted some fascinating phenomena, especially for large values of p [41]. However, these results are different from those based on the system, since they are inactive as regards producing ferromagnetic ordering.…”

Section: Discussionmentioning

confidence: 99%

Differential Operator Technique in the Ising Spin Systems

1993

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“…The Hamiltonian is given by (1). As discussed in previous works [l to 3, 7, 81, the starting point for the statistics of the system is the spin-one exact identities At this stage, in order to write (3) and (4) in a form which is particularly amenable to approximation, let us introduce the differential operator technique [ 101 as follows:…”

Section: Formulationmentioning

confidence: 99%