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Butera, P.; Pernici, M.

doi:10.1016/j.physa.2018.05.010

Cited by 33 publications

(39 citation statements)

References 71 publications

(186 reference statements)

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“…Note that it agrees with the MC results surprisingly well, while the MFA dependence 2 for critical temperature of the AFM ordering given by (17) becomes improper at |n| > 0.5. The concentration dependence similar to our T P S (n) was found numerically for Blume-Capel model [49] by intersecting the low-temperature and high-temperature expansions of the free-energy.…”

Section: Critical Temperature Of the Spin-charge Separationsupporting

confidence: 83%

Phase diagrams of a 2D Ising spin-pseudospin model

Panov

Ulitko

Budrin

et al. 2019

Journal of Magnetism and Magnetic Materials

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We consider the competition of magnetic and charge ordering in high-Tc cuprates within the framework of the simplified static 2D spin-pseudospin model. This model is equivalent to the 2D dilute antiferromagnetic (AFM) Ising model with charged impurities. We present the mean-field results for the system under study and make a brief comparison with classical Monte Carlo (MC) calculations. Numerical simulations show that the cases of strong exchange and strong charge correlation differ qualitatively. For a strong exchange, the AFM phase is unstable with respect to the phase separation (PS) into the charge and spin subsystems, which behave like immiscible quantum liquids. An analytical expression was obtained for the PS temperature.The Hamiltonian of the static spin-pseudospin model is:where S zi is a z-projection of the on-site pseudospin S = 1 and σ zi = P 0i s zi /s is a normalized z-projection of conventional spin s = 1/2 operator, multiplied by the projection operator P 0i = 1 − S 2 iz . The ∆ = U/2 is the on-site correlation and V > 0 is the inter-site density-density interaction, J =J/s 2 > 0 is the Cu 2+ −Cu 2+ Ising spin exchange coupling, h =h/s is the external magnetic field, µ is the chemical potential, so we assume the total charge constraint, nN = S zi = const, where n is the density of doped charge. The sums run over the sites of a 2D square lattice, ij means the nearest neighbors. This spin-pseudospin model generalizes the 2D dilute AFM Ising model with charged impurities. In the limit ∆ → −∞ it reduces to the S = 1 2 Ising model with fixed magnetization. At ∆ > 0 the results can be compared with the Blume-Capel model [27,28,29] or with the Blume-Emery-Griffiths model [30].An analysis of the ground state (GS) phase diagrams was done within the mean field approach [24,25]. It was shown, that the five GS phases are realized in two limits. In a weak exchange limit, atJ < V , all the GS phases (COI, COII, COIII, FIM) correspond to the charge ordering (CO) of a checker-board type at mean charge density n. While the COI phase is the charge-ordered one without spin centers, the COII and COIII phases are diluted by the non-interacting spins distributed in one sublattice only. This ferrimagnetic spin ordering is a result of the mean-field approach, so the classical MC calculations show a paramagnetic response at low temperatures. The FIM phase is also formally ferrimagnetic. Here the AFM spin ordering is diluted by the non-interacting charges distributed in one sublattice. In a strong exchange limit, atJ > V , there are only COI phase and AFM phase with the charges distributed in both sublattices. The absence of charge transfer in the Hamiltonian (1) is the most important limitation of our present model for comparison with the actual phase diagram of cuprates. But, as shown in [31], the accounting for two-particle transport enriches the GS phase diagram of the spin-pseudospin model with superfluid and supersolid phases competing with CO phases.The paper is organized as follows. We present the mean-field result...

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Section: Critical Temperature Of the Spin-charge Separationsupporting

confidence: 83%

Phase diagrams of a 2D Ising spin-pseudospin model

Panov

Ulitko

Budrin

et al. 2019

Journal of Magnetism and Magnetic Materials

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“…BEP has been comparatively less observed and studied in literature. Two well known examples where BEP has been observed are: anisoptropic continuous spin systems as a spin flop [28] and in spin 3/2 systems with crystal field [30,31]. The emergence of BEP as a consequence of disorder is a new result being presented in this paper.…”

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confidence: 78%

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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“…The region becomes narrower as it approaches the TP (see, for example, [16] D/J = 2.84479(30) and k B T /J = 1.4182(55)) for the tricritical coupling ratio, which is a "foreshadowing" of the crossover effects. After this point, it becomes even narrower, and this is only an "echo" of the critical region since one expects only a first-order transition for D/J ≥ 2.8502 [17] and in this case, out of figure since this first-order transition point The points obtained with the optimization in (a) compared with the curve obtained by Butera and Pernici [17].…”

mentioning

confidence: 90%

“…Nevertheless, the optimal points are indeed the critical line points? By using the critical points presented in Butera and Pernici [17] obtained via low and hightemperature expansions (see table 5 in this reference), we can check if our critical points are precisely well estimated.…”

mentioning

confidence: 98%

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First numerical evidence of Janssen-Oerding's prediction in a three-dimensional spin model far from equilibrium

da Silva

2021

Preprint

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predicted an interesting anomalous tricritical dynamic behavior in three-dimensional models via renormalization group theory. However, we verify a lack of literature about the computational verification of this universal behavior. Here, we used some tricks to capture the log corrections and the parameters predicted by these authors using the three-dimensional Blume-Capel model. In addition, we also performed a more detailed study of the dynamic localization of the phase diagram via power laws optimization. We quantify the crossover phenomena by computing the critical exponents near the tricritical point.

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The Blume–Capel model for spins S=1 and 3∕2 in dimensions

Cited by 33 publications

References 71 publications

Phase diagrams of a 2D Ising spin-pseudospin model

Phase diagrams of a 2D Ising spin-pseudospin model

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

First numerical evidence of Janssen-Oerding's prediction in a three-dimensional spin model far from equilibrium

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