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

Sumedha,; Mukherjee, Soheli

doi:10.1103/physreve.101.042125

Cited by 18 publications

(15 citation statements)

References 56 publications

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“…This was observed in the recent work of Ref. [61] for the present model in a fully connected graph, where p * ≈ 0.1 was found. Irrespective of the underlying graph topology of these analytical results, the effect of disorder in the first-order transition regime of the pure model can therefore only be addressed in transitions occurring in the vicinity of the tricritical point or for the T < T t temperature range, or even in a more controlled set of parameters for simulations in the small p-limit (say for p ≤ 0.1).…”

Section: Model and Methodssupporting

confidence: 88%

“…In the current work we provide additional evidence in favor of the strong universality hypothesis, by studying the Blume-Capel model but with a different type of quenched randomness in the crystal-field coupling parameter. A site-dependent crystal-field coupling has also been used in the past by Branco and Boechat [59] and more recently by Sumedha and Mukherjee [61] and is much closer to the experimental reality, as it mimics the physics of random porous media (mainly aerogels) in 3 He- 4 He mixtures [60]. We employed extensive numerical simulations using a parallel implementation of the Wang-Landau algorithm [62], as outlined in the following Sec.…”

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confidence: 99%

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Ising universality in the two-dimensional Blume-Capel model with quenched random crystal field

Vatansever,

Theodorakis

et al. 2020

Preprint

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Using high-precision Monte-Carlo simulations based on a parallel version of the Wang-Landau algorithm and finite-size scaling techniques we study the effect of quenched disorder in the crystalfield coupling of the Blume-Capel model on the square lattice. We mainly focus on the part of the phase diagram where the pure model undergoes a continuous transition, known to fall into the universality class of the pure Ising ferromagnet. A dedicated scaling analysis reveals concrete evidence in favor of the strong universality hypothesis with the presence of additional logarithmic corrections in the scaling of the specific heat. Our results are in agreement with an early real-space renormalization-group study of the model as well as a very recent numerical work where quenched randomness was introduced in the energy exchange coupling. Finally, by properly fine tuning the control parameters of the randomness distribution we also qualitatively investigate the part of the phase diagram where the pure model undergoes a first-order phase transition. For this region, preliminary evidence indicate a smoothening of the transition to second-order with the presence of strong scaling corrections.

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Section: Model and Methodssupporting

confidence: 88%

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confidence: 99%

Ising universality in the two-dimensional Blume-Capel model with quenched random crystal field

Vatansever,

Theodorakis

et al. 2020

Preprint

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“…The frustration introduced by the repulsive biquadratic interaction makes it a very interesting model to study. In fact we find that the phase diagram for the repulsive(−1 < K ≤ 0) BEG model is similar to the topology of the phase diagram of the Blume Capel model with random crystal field order studied resently [34] for the intermediate and weak disorder. In this paper, we have looked at the ensemble inequivalence not just by looking at the first order line in the (T, ∆) plane but also by computing the critical lines(λ ± ) in the H = 0 plane.…”

Section: Introductionsupporting

confidence: 70%

“…Disorder, in general, is known to smoothen the first order transition and has been known to convert a TCP into a BEP [34]. We studied a pure BEG model here.…”

Section: Discussionmentioning

confidence: 99%

Phase diagram of the repulsive Blume-Emery-Griffiths model in the presence of external magnetic field on a complete graph

Mukherjee,

Sadhu

2020

Preprint

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For the repulsive Blume-Emery-Griffiths model the phase diagram in the space of three fields, temperature (T ), crystal field (∆) and magnetic field (H), is computed on a fully connected graph, in the canonical and microcanonical ensembles. When the strength of the biquadratic interaction (K) is low, there exists a tricritical point where the three critical lines meet. As K decreases, new multicritical points like the critical end point and bicritical end point arise in the (T, ∆) plane. For K > −1, we observe that the two critical lines in the H plane and the multicritical points are different in the two ensembles. At K = −1, the two critical lines in the H plane disappear and as K decreases further, we see no phase transition in the H plane. Exactly at K = −1 the two ensembles become equivalent. Beyond that for all K < −1, there are no multicritical points and there is no ensemble inequivalence in the phase diagram. We also study the transition lines in the H plane for positive K i.e. for attractive biquadratic interaction. We find that the transition lines in H plane are not monotonic in temperature for large positive K.

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“…At TCP the line of continuous transitions (known as the λ line) given by Eq. 17 meets the two other lines of continuous transitions in the T − ∆ − H space [36,49]. These are the λ ± lines.…”

Section: Finite Temperature Phase Diagram a Trimodal Distributionmentioning

confidence: 87%

Phase transitions in the Blume-Capel model with trimodal and Gaussian random fields

Mukherjee

2022

Preprint

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We obtain the phase diagram for the infinite range random field Blume capel (RFBC) model for the symmetric trimodal distribution of the random field (h) in the temperature (T )-crystal field (∆) and T − h planes. We find 4 ordered and 2 disordered phases in the model at T = 0. Depending on the disorder strength, there are 5 different ground state phase diagrams in the ∆ − h plane. The T − ∆ and T − h phase diagrams also can be classified into 5 different categories as a function of the strength of the disorder, consistent with the 5 different ground state phase diagrams. The phase diagrams at finite temperature consist of lines of first order and second order transitions, multicritical points like tricritical point, bicritical points, critical end point, and also many multiphase coexistence points. We find re-entrance in the T −h phase diagram for the symmetric trimodal distribution for some values of ∆. We also studied the Gaussian distribution of the random field. In contrast, the ground state for the Gaussian distribution consists of only one ordered and one disordered phase. At low disorder strength (σ) the T − ∆ phase diagram has a line of first order and a line of second order transitions, separated by a TCP. However at higher σ the phase diagram only has a line of second order transition. In general the phase diagram of the random field problems is expected to be similar for symmetric distributions as has been observed for the random field O(n) models. In the case of RFBC we find that while for Gaussian distribution, the phase diagram is similar to the phase diagram of the infinite range random field Ising model (RFIM) with the bimodal random field distribution, for the symmetric trimodal distribution there are many different T − ∆ and T − h phase diagrams with multiple multicritical and multi-phase coexistence points.

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

Cited by 18 publications

References 56 publications

Ising universality in the two-dimensional Blume-Capel model with quenched random crystal field

Ising universality in the two-dimensional Blume-Capel model with quenched random crystal field

Phase diagram of the repulsive Blume-Emery-Griffiths model in the presence of external magnetic field on a complete graph

Phase transitions in the Blume-Capel model with trimodal and Gaussian random fields

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