Mean-field solution of the Blume–Capel model under a random crystal field

Santos, P. V.; Costa, F. A. da; Araújo, João M. de

doi:10.1016/j.physleta.2015.03.029

Cited by 22 publications

(22 citation statements)

References 29 publications

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“…Blume-Capel model is a very useful model due to its simplicity and rich phase diagram. While its phase diagram in the presence of disorder in (T, ∆) plane has been studied using many different techniques like renormalisation group techniques [21], field theories [20],Bethe lattice [22],replica [26] and numerical methods [41], the three field phase diagram has not been studied. In this paper, we found a BEP in the phase diagram of Blume-Capel model with bimodal random crystal field on a fully connected graph by looking at the three field (T, ∆, H) phase diagram.…”

Section: Discussionmentioning

confidence: 99%

“…In two dimensions it was shown that even an infinitesimal amount of random field disorder can change a first order transition to continuous transition or can destroy it altogether [17,18]. Most of the previous studies of random crystal field Blume-Capel model have focussed on (T, ∆) plane [19][20][21][22][23][24][25][26][27]. In this paper, we revisit the problem and look at the phase diagram in the three fields space.…”

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confidence: 99%

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Emergence of a bicritical end point in the random-crystal-field Blume-Capel model

Sumedha

Mukherjee

2020

Phys. Rev. E

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We obtain the phase diagram for the Blume-Capel model with bimodal distribution for random crystal fields, in the space of three fields: temperature(T ), crystal field(∆) and magnetic field (H). We find that three critical lines meet at a tricritical point, but only for weak disorder. As disorder strength increases there is no tricritical point in the phase diagram. We instead find a bicritical end point, where only two of the critical lines meet on a first order surface in the H = 0 plane. For intermediate strengths of disorder, the phase diagram has critical end points along with the bicritical end point. One needs to look at the phase diagram in the space of three fields to identify various such multicritical points.

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

Emergence of a bicritical end point in the random-crystal-field Blume-Capel model

Sumedha

Mukherjee

2020

Phys. Rev. E

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“…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%

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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“…The interplay between quenched disorder provided by a random field and network connectivity in the BC model is investigated by using the replica method [33]. Moreover, the BC model with infinite-range ferromagnetic interactions and under the influence of a quenched disorder has been investigated and a classification of the phase diagrams in terms of their topology is presented in [34].…”

Section: Introductionmentioning

confidence: 99%

Acoustic Signatures of the Phases and Phase Transitions in the Blume Capel Model with Random Crystal Field

Gulpinar

2018

Advances in Condensed Matter Physics

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Sound propagation in the Blume Capel model with quenched diluted single-ion anisotropy is investigated. The sound dispersion relation and an expression for the ultrasonic attenuation are derived with the aid of the method of thermodynamics of irreversible processes. A frequency-dependent dispersion minimum that is shifted to lower temperatures with rising frequency is observed in the ordered region. The thermal and sound frequency (ω) dependencies of the sound attenuation and effect of the Onsager rate coefficient are studied in low- and high-frequency regimes. The results showed that ωτ≪1 and ωτ≫1 are the conditions that describe low- and high-frequency regimes, where τ is the single relaxation time diverging in the vicinity of the critical temperature. In addition, assuming a linear coupling of sound wave with the order parameter fluctuations in the system and ε as the temperature distance from the critical point, we found that the sound attenuation follows the power laws α(ω,ε)~ω2ε-1 and α(ω,ε)~ω0ε1 in the low- and high-frequency regions, while ε→0. Finally, a comparison of the findings of this study with previous theoretical and experimental studies is presented and it is shown that a good agreement is found with our results.

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Mean-field solution of the Blume–Capel model under a random crystal field

Abstract: In this work we investigate the Blume-Capel model with infinite-range ferromag-

Cited by 22 publications

References 29 publications

Emergence of a bicritical end point in the random-crystal-field Blume-Capel model

Emergence of a bicritical end point in the random-crystal-field Blume-Capel model

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

Acoustic Signatures of the Phases and Phase Transitions in the Blume Capel Model with Random Crystal Field

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