Monte Carlo study of the spin-1 Blume–Capel Ising film

Using Monte Carlo simulations with the Metropolis algorithm, we have studied the influence of crystal-field interaction on the critical behavior of magnetic spin-1 Ising film on a cubic lattice structure. The phase diagrams in the (_kBTc/J,R=_Js/J)$(k_{\mathrm{B}}{T}_{\mathrm{c}}/J,R=J_{\mathrm{s}}/J)$ plane are obtained for different values of the crystal-field interaction. We found that the special point _Rsp(_Rc)$R_{\mathrm{sp}}(R_{\mathrm{c}})$, at which the critical temperature is independent of the film thickness N, is independent of the crystal-field interaction and that the system may exhibit a tricritical behavior.     

Projected-wave-function study of the spin-1/2 Heisenberg model on the Kagomé lattice

We perform a Gutzwiller projected-wave-function study for the spin-1/2 Heisenberg model on the Kagomé lattice to compare energies of several spin-liquid states. The result indicates that a U(1)-Dirac spin-liquid state has the lowest energy. Furthermore, even without variational parameters, the energy turns out to be very close to that found by exact diagonalization. We show that such a U(1)-Dirac state represents a quantum phase whose low-energy physics is governed by four flavors of two-component Dirac fermions coupled to a U(1) gauge field. These results are discussed in the context of recent experiments on ZnCu(3)(OH)(6)Cl(2).     

Study of the first-order transition in the spin-1 Blume–Capel model by using effective-field theory

The spin-1 Blume–Capel model on a square lattice is studied by using an effective-field theory (EFT) with correlation. We propose an expression for the free energy within the EFT. The phase diagram is constructed in the temperature (T) and single-ion anisotropy amplitude (D) plane. The first-order transition line is obtained by Maxwell construction (comparison between free energies). Our results predict first-order transitions at low temperatures and large anisotropy strengths, which correspond in the phase diagram to the existence of a tricritical point (TCP). We compare our results with mean-field approximation (MFA), that show a qualitative correct behavior for the phase diagram.     

Nonequilibrium behavior of the kinetic metamagnetic spin-5/2 Blume–Capel model

The dynamic magnetic behavior of the kinetic metamagnetic spin-5/2 Blume–Capel model is examined, within a mean-field approach, under a time-dependent oscillating magnetic field. To describe the kinetics of the system, Glaubertype stochastic dynamics has been utilized. The mean-field dynamic equations of the model are obtained from the Master equation. Firstly, these dynamic equations are solved to find the phases in the system. Then, the dynamic phase transition temperatures are obtained by investigating the thermal behavior of dynamic sublattice magnetizations. Moreover, from this investigation, the nature of the phase transitions(first- or second-order) is characterized. Finally, the dynamic phase diagrams are plotted in five different planes. It is found that the dynamic phase diagrams contain the paramagnetic(P),antiferromagnetic(AF5/2, AF3/2, AF1/2) phases and five different mixed phases. The phase diagrams also display many dynamic critical points, such as tricritical point, triple point, quadruple point, double critical end point and separating point.     

Position space renormalization group study of the spin-1 random semi-infinite Blume–Capel model

We study the spin-1 Blume–Capel model under a random crystal field in the tridimensional semi-infinite case. This has been done by using the real-space renormalization group approximation and specifically the Migdal–Kadanoff technique. Interesting results are obtained, which tell us that the randomness destroys the first order phase transitions and only those of the second order occur. We give the list of nine fixed points and their topology describing the surface critical behavior. Five new types of phase diagram are found with a rich variety of phase transitions, in accordance with the values of the bulk and surface probabilities and the ratios linking bulk and surface interactions.     

Geometric phase of spin-1 in a rotating magnetic field

The quantum phase and the related fields have attracted considerable attention. The geometric phase of spin-1/2 particle in the magnetic field has been discussed comprehensively, but few of spin-1. In this paper, the exact solution of spin-1 was obtained by using rotational frame method. The problems of the Rabi oscillation, dynamical phase, and geometric phase were solved.     

Influence of transverse field on the spin-3/2 Blume–Capel model on rectangular lattice

Transverse field effect on thermodynamic properties of the spin-3/2 Blume–Capel model on rectangular lattice in which the interactions in perpendicular directions differ in signs is studied within the mean field approximation. Phase diagrams in the (transverse field, temperature) plane are constructed for various values of single-ion anisotropy.     

Néel order in the ground state of spin-1/2 Heisenberg antiferromagnetic multilayer systems

We show existence of Néel order for the ground state of a system withM two-dimensional layers with spin 1/2 and Heisenberg antiferromagnetic coupling, providedM8. The method uses the infrared bounds for the ground state combined with ideas introduced by Kennedy, Lieb, and Shastry.     

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.     

Spin polarizabilities and characteristics of spin-1 hadrons related to parity nonconservation in the Duffin–Kemmer–Petiau formalism

Spin polarizabilities of spin-1 particles typical of spin-1/2 hadrons are established within the Duffin–Kemmer–Petiau formalism using the relativistically invariant effective tensor representation of Lagrangians of two-photon interaction with hadrons. New spin polarizabilities of spin-1 particles associated with the presence of tensor polarizabilities are also determined.     

Covariant quantization of “massive” spin-\frac{3}{2} fields in the de sitter space

We present a covariant quantization of the free “massive” spin- $\frac{3}{2}$ fields in four-dimensional de Sitter space-time based on analyticity in the complexified pseudo-Riemannian manifold. The field equation is obtained as an eigenvalue equation of the Casimir operator of the de Sitter group. The solutions are calculated in terms of coordinate-independent de Sitter plane-waves in tube domains and the null curvature limit is discussed. We give the group theoretical content of the field equation. The Wightman two-point function $S^{i \bar{j}}_{\alpha\alpha'}(x,x')$ is calculated. We introduce the spinor-vector field operator Ψ _α (f) and the Hilbert space structure. A coordinate-independent formula for the field operator Ψ _α (x) is also presented.     

Collision dynamics between stretched states of spin-2 87Rb Bose–Einstein condensates

We experimentally observed the time dependence of the spin populations of spin-2 ⁸⁷Rb Bose–Einstein condensates confined in an optical trap. The condensed atoms were initially populated in the stretched states |F=2,m _F =+2〉 and |F=2,m _F =?2〉 with several varieties of population imbalances. No spin-exchange collisions were observed in a weak magnetic field of 45 mG. The atom loss rate depended on the observed relative population of spin-states. We calculated the loss rate due to two-body inelastic collisions with the population imbalance using an experimentally estimated rate of 17.0(±1.9)×10^?14 cm³?s^?1 under the population balance. The calculations were in good agreement with the measurements. Our results show that the dependence of inelastic collisions on spin channels plays an important role in the time-evolution of spin populations.