Spin-1 Blume-Capel Model Research Articles

Anomalous thermodynamics in a mixed spin-1/2 and spin-1 hexagonal nanowire system

The mixed spin-1/2 Ising model and spin-1 Blume–Capel model in an hexagonal nanowire structure under the presence of crystal field is considered. The free energy is obtained through the transfer matrix technique, which is solved numerically. Our main result lies in the presence of pseudo-transition in low temperature region near the ferrimagnetic/ferromagnetic boundary, due to the influence of a crystal field. The evidence of a pseudo-transition is observed in several quantities. Free energy first derivative quantities like entropy and internal energy show an abrupt but continuous jump, whereas quantities associated with second derivatives of the free energy like the specific heat exhibit a strong sharp peak, quite similar to a second order phase transition. We also investigate magnetization patterns and do not find evidence of spontaneous magnetization. Nevertheless, assuming a small magnetic field, we can induce a magnetization which resembles a spontaneous magnetization at a pseudo-critical temperature.

Theoretical analysis of magnetic properties and the magnetocaloric effect using the Blume-Capel model

This work investigates the magnetic properties and the magnetocaloric effect in the spin-1 Blume-Capel model. The study was carried out using the mean-field theory from the Bogoliubov inequality to obtain the expressions of free energy, magnetization and entropy. The magnetocaloric effect was calculated from the variation of the entropy obtained by the mean-field theory. Due to the dependence on the external magnetic field and the anisotropy included in the model, the results for the magnetocaloric effect provided the system with first-order and continuous phase transitions. To ensure the results, the Maxwell relations were used in the intervals where the model presents continuous variations in magnetization and the Clausius-Clapeyron equation in the intervals where the model presents discontinuity in the magnetization. The methods and models for the analysis of a magnetic entropy change and first-order and continuous magnetic phase transitions, such as mean-field theory and the Blume-Capel model, are useful tools in understanding the nature of the magnetocaloric effect and its physical relevance.

Critical properties of the spin-1 Blume–Capel model with a random transverse crystal field

The random transverse crystal field (RTCF) chosen to be along the x-axis is applied to the spin-1 Blume–Capel (BC) model and the mean-field approximation (MFA) is employed to investigate the behaviors of order-parameters and to obtain its phase diagrams. The selected form of the RTCF is in a bimodal form which is either turned on with probability p or turned off with 1−p on the sites of spin-1. The effects of the longitudinal and transverse crystal fields, i.e. Dz and Dx respectively, number of nearest-neighbors (NN) q, bilinear exchange interaction parameter J between the NN spins along the z-axis and temperature are analyzed in detail. The emphasis is given to the square lattice with q=4. It is found that the model displays first- and second-order phase transitions with the existence of tricritical point (TCP), critical end-points (CEP) and end-points (EP).

Yang-Lee edge singularity triggered entanglement transition

We show that a class of $\mathcal{PT}$ symmetric non-Hermitian Hamiltonians realizing the Yang-Lee edge singularity exhibits an entanglement transition in the long-time steady state evolved under the Hamiltonian. Such a transition is induced by a level crossing triggered by the critical point associated with the Yang-Lee singularity and hence is first-order in nature. At the transition, the entanglement entropy of the steady state jumps discontinuously from a volume-law to an area-law scaling. We exemplify this mechanism using a one-dimensional transverse field Ising model with additional imaginary fields, as well as the spin-1 Blume-Capel model and the three-state Potts model. We further make a connection to the forced-measurement induced entanglement transition in a Floquet non-unitary circuit subject to continuous measurements followed by post-selections. Our results demonstrate a new mechanism for entanglement transitions in non-Hermitian systems harboring a critical point.

The mixed spin-3/2 and spin-2 Blume-Capel model by renormalization group approach

PurposeThe authors investigate the magnetic properties of a mixed spin-3/2 and spin-2 Blume-Capel model on square and cubic lattices with two different single-ion anisotropies.Design/methodology/approachTo study the critical behavior of a mixed spin-3/2 and spin-2 system, the authors have used a real space renormalization group approximation and specifically the Migdal-Kadanoff technique. The authors give the phase diagrams for two different cases: (1) on the (Δ/|J|, 1/|J|) plane with ΔA = ΔB = Δ, and (2) on the (ΔA/|J|, 1/|J|) and (ΔB/|J|, 1/|J|) planes for selected values of ΔB/|J| and ΔA/|J|, respectively.FindingsThe phase diagrams obtained show that the system exhibits both second- and first-order phase transitions as well as tricritical points for some values of the anisotropies. Moreover, using the variation of the free energy and its derivative at low temperatures, the authors have seen the appearance of first-order transitions at very low temperatures.Originality/valueFew investigations of mixed spin-3/2 and spin-2 systems with crystal field have been realized. For this reason, the authors use the renormalization group approach to complete the work done on these systems. In absence of an exact solution, this contributes to the synthesis of the approximation results on mixed spins models.

Dimensionality Effects on the Mixed Spin-1/2 and Spin-2 Blume-Capel Model: Renormalization Group Theory

Dimensionality Effects on the Mixed Spin-1/2 and Spin-2 Blume-Capel Model: Renormalization Group Theory

Random crystal field effects on antiferromagnetic spin-1 Blume–Capel model

The outcome of the random crystal field effects on the antiferromagnetic spin-1 Blume–Capel model and external magnetic field are examined on the Bethe Lattice in terms of exact recursion relations. It is assumed that the crystal field is either turned on or off randomly with probability [Formula: see text] and [Formula: see text], respectively. The phase diagrams are constructed from the thermal analysis of the order parameters with the coordination number [Formula: see text] which corresponds to honeycomb lattice. It is explored that the system goes both second- and first-order phase transitions, along with the reentrant behavior and a few critical points. The reentrant behavior is stronger for lower values of [Formula: see text] and disappears as [Formula: see text] gets closer to 1.0. The first-order lines are observed to be either linked to the tricritical points or decomposed. The critical end points and double critical points are also observed.

Effective-field theory identity for studying first order phase transitions of Ising-like spin models

An effective-field theory identity (EFTI) for studying first order phase transitions of Ising-like spin models is proposed. Via an analytical study, this identity can be used to obtain the phase transitions between two distinct states that presents the same free energy value. In order to show the results obtained by the application of the EFTI, the phase diagram of the spin-1 Blume-Capel model is constructed for the hexagonal, square and cubic lattices. For the cubic lattice, some magnetizations and quadrupoles curves are also presented.

The random field Blume-Capel model on the Bethe lattice

The spin-1 Blume-Capel model is studied under the effect of a bimodal random magnetic field with equal probabilities on the Bethe lattice in terms of the exact recursion relations. The turning of magnetic field up or down with equal probability is the key of this work, since in this case one can observe the occurrence of phase transitions in contrary to the continuous magnetic field acting on the same model. Therefore, the phase diagrams are calculated on the crystal field-temperature planes for given values of the random magnetic field with the coordination numbers z=3,4 and 6. It is found that the model does give both second- and first-order phase transitions in addition to the tricritcal and another type of a critical point.

A novel critical behavior of the spin-1 Blume–Capel model with a distance-dependent nearest-neighbor exchange interaction and magneto-elastic coupling

A generalized spin-1 Blume–Capel model with distance/volume dependent nearest-neighbor exchange interaction is introduced and investigated using the standard methods of statistical mechanics. Besides of the volume-dependent magnetic energy, the static electromagnetic energy and anharmonic Einstein phonon contribution are also taken into account. Taking the simple volume dependence of all energy contributions we have obtained the equation of state, magnetic moment, internal and Helmholtz free energy of the system. The ground-state and finite-temperature phase diagrams are obtained and discussed in detail. Is it shown that the generalized spin-1 Blume–Capel model exhibits a novel critical behavior appearing due to magnetostriction and thermal volume variations. The presented approach is very universal and easily applicable to many other theoretical models in different fields of solid state physics.

Physical observable for one-dimensional the spin-1 Blume–Capel model

We carry out an extensive study, within the infinite matrix product state algorithm, one-dimensional spin-1 Blume–Capel model on the spin-chain and subject to a changeable external magnetic field. The phase transition points are obtained by investigating the behavior of physical observable and as well as exacting the critical exponent from the scaling relationship. The final results are achieved for the physical observable-quantum entanglement entropy, local order parameter and its scaling: the scaling relationship between quantum entanglement entropy and truncation dimension, the scaling of Schmidt decomposition coefficient λmax and truncation dimension, the critical exponent of local order parameter near the phase transition point is extracted with the scaling behavior for the model with exchange coupling γ=0.6. These techniques are an easy way to exact the critical exponent for quantum phase transitions.

The mixed spin-1/2 and spin-1 model with alternating coordination number

The mixed spin-1/2 and spin-1 Blume–Capel model is studied with randomly alternated coordination numbers (CN) on the Bethe lattice (BL) by utilizing the exact recursion relations. Two different CNs are randomly distributed on the BL by using the standard–random (SR) approach. It is observed that this model presents first-order phase transitions and tricritical points for variations of CNs 3 and 4, even if these behaviors are not displayed for the regular mixed-spin on the BL. The phase diagrams are mapped by obtaining the phase transition temperatures of the first- and second-order on several planes.

Finite Temperature Phase Diagrams of the Mixed Spin-1 and Spin-2 Blume–Capel Model by Renormalization Group Approach

The Blume–Capel model with mixed spins S = 1 and S = 2, on d-dimensional hypercubic lattice, is studied using the real space renormalization group approximation and specifically the Migdal–Kadanoff technique. We give the phase diagrams on the (Δ1/|J|, 1/|J|) and (Δ2/|J|, 1/|J|) planes which are studied for selected values of Δ2/|J| and Δ1/|J| respectively, with first and second order phase transitions and tricritical points. Also, the associated fixed points are drawn up in a table, and by linearizing the transformation at the vicinity of these points, we determine the critical exponents for d = 2 and d = 3. In particular, we find that the system under study may exhibit reentrant phenomenon.

Ferromagnetic phases due to competing short- and long-range interactions in the spin-5/2 and spin-2 Blume–Capel model

We broaden the study of the statistical physics of the spin-S Blume–Capel model with ferromagnetic mean-field interactions J in competition with short-range antiferromagnetic interactions K in a linear chain in the thermodynamic limit. This work is dedicated to the case when S takes the half-integer spin S=5/2 and when S assumes the integer value S=2. In both cases the phase diagrams exhibit new ferromagnetic phases (for certain values of K) enclosed by branches emerging from the first-order frontiers of the pure ferromagnetic model. For finite temperatures the complex topologies were obtained by numerical minimization of the free energy and some results were confirmed by Monte Carlo simulations.

Monte Carlo study of a layering transition with spin-1 Blume–Capel model under crystal field effect

The crystal field effect on the layering transitions of the spin-1 Blume–Capel model is studied, in the presence of external and surface magnetic field, using Monte Carlo simulations. The ground state phase diagrams were determined analytically. We showed that existing phases are strongly dependent on the surface and the bulk crystal field. At finite temperature, the phase diagrams have been examined in detail. In particular, different phases are found to be separated for different configurations. To complete this study, we discuss and interpret the behavior of the magnetizations and the quadrupolar moments.

The random distribution of the coordination numbers in the mixed spin-1/2 and spin-2 Blume-Capel model

The effects of random distribution of coordination numbers are investigated for the mixed spin-1/2 and spin-2 Blume-Capel model on the Bethe lattice in terms of exact recursion relations. The usual coordination numbers, i.e. q=3,4 and 6, corresponding to the honeycomb, square and simple cubic lattices, respectively, are considered. Two different q values are taken as couples and are varied randomly in terms of a standard-random approach on the shells of the Bethe lattice with some probabilities. It is found that the model gives either first- or second-order phase transitions for appropriate values of probability (p) and single ion anisotropy (d). One or two tricritical points are also observed depending on the given values of p and d, respectively.

The Random Change of Coordination Number in the Blume-Capel Model

The spin-1 Blume-Capel model is investigated under the random change of coordination numbers on the Bethe lattice (BL). Various coordination numbers are taken as couples and varied randomly on the shells of the BL. The randomization is realized in the standard-random approach and the formulation is obtained in terms of exact recursion relations. The phase diagrams are obtained by calculating the places of the second- and first-order phase transitions and tricritical points.

A new effective correlation mean-field theory for the ferromagnetic spin-1 Blume–Capel model in a transverse crystal field

A new approximation technique is developed so as to study the quantum ferromagnetic spin-1 Blume–Capel model in the presence of a transverse crystal field in the square lattice. Our proposal consists of approaching the spin system by considering islands of finite clusters whose frontiers are surrounded by noninteracting spins that are treated by the effective-field theory. The resulting phase diagram is qualitatively correct, in contrast to most effective-field treatments, in which the first-order line exhibits spurious behavior by not being perpendicular to the anisotropy axis at low-temperatures. The effect of the transverse anisotropy is also verified by the presence of quantum phase transitions. The possibility of using larger sizes constitutes an advantage to other approaches where the implementation of larger sizes is computationally costly.

The spin-1 Blume–Capel model on the Bethe lattice in ± J distribution with an adjustable parameter between FM and AFM phases

The spin-1 Blume–Capel (BC) model is studied on the Bethe lattice (BL) for the ± J distribution with a competing adjustable parameter α which alters the strength of bilinear exchange interaction parameter for the ferromagnetic phase (J > 0) with respect to antiferromagnetic phase (J < 0). The J > 0 and αJ < 0 values are also distributed throughout the BL with probabilities p and 1−p, respectively. The order-parameters are obtained on the BL in terms of exact recursion relations (ERR’s) and their temperature (T) variations are studied to calculate the phase diagrams on the (α, T) planes for given values of p, crystal field (D) and coordination number q=3 corresponding to honeycomb lattice. It is found that the model gives both first- and second-order phase transitions and also tricritical points. In addition to the well known ordinary phases and TCP’s, the spin glass phase and two more special points are also observed.

Dynamic hysteresis behaviors in the kinetic Ising system on triangular lattice

ABSTRACTWe studied dynamic hysteresis behaviors of the spin-1 Blume-Capel (BC) model in a triangular lattice by means of the effective-field theory (EFT) with correlations and using Glauber-type stochastic dynamics. The effects of the exchange interaction (J), crystal field (D), temperature (T) and oscillating frequency (w) on the hysteresis behaviors of the BC model in a triangular lattice are investigated in detail. Results are compared with some other dynamic studies and quantitatively good agreement is found.