Effect of single-ion uniaxial anisotropy on the phase diagrams of magnetic system in the presence of internal spin fluctuation

Basing on the two-spin-per-site Heisenberg model, the effect of single-ion uniaxial anisotropy on the phase diagrams of magnetic system in the presence of internal spin fluctuation has been investigated by use of the mean field theory. It was found that single-ion uniaxial anisotropy has important effect on the phase digrams. In the ferromagnetic case (J₃>0) the positive single-ion uniaxial anisotropies (D) suppress the internal spin fluctuation and raise the phase trasition temperature, and negative single-ion uniaxial anisotropies (D) increase the internal spin fluctuation and reduce the phase trasition temperature. In the antiferromagnetic case (J₃<0), there exist two critical values J_c1 and J_c2 (|J_c2|<|J_c1|) in the positive D values. In the |J₃|<|J_c2| range intra-spin exchange coupling prevails inter-spin exchange coupling, the positive D values suppress the internal spin fluctuation and raise the phase transition temperature. In the |J₃|>|J_c1| range the two sub-spins behave as a rigid spin and the positive D values make the reduction of the phase transition temperature. We also observe that the larger D values make the range of internal spin fluctuation to move towards the larger |J₃| range.     

Phase diagrams of competing quadruple and binary interactions on Cayley tree-like lattice: Triangular Chandelier

We study the phase diagrams for the Ising model on a Cayley tree-like lattice, called Triangular Chandelier, with competing nearest-neighbour interactions J₁, prolonged next-nearest-neighbour interactions J_p and one-level next-nearest-neighbour quadruple interactions J_l1. The phase diagrams display the multicritical points (the Lifshitz points) that are at nonzero temperature and many modulated phases. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established; it recovers, as particular case, previous work of Vannimenus extension result given by Ganikhodjaev and U?uz for k=3. At vanishing temperature, the phase diagram is fully determined for all values and signs of J₁,J_p and J_l1. At finite temperatures several interesting features are exhibited for typical values of J_l1/J₁ and −J_p/J₁.     

Low-energy singlet sector in the spin-1/2 <Emphasis Type="Italic">J</Emphasis><Subscript>1</Subscript>–<Emphasis Type="Italic">J</Emphasis><Subscript>2</Subscript> Heisenberg model on a square lattice

Based on a special variant of the plaquette expansion, an operator is constructed whose eigenvalues give the low-energy singlet spectrum of a spin-\(\frac{1}{2}\) Heisenberg antiferromagnet on a square lattice with nearest-heighbor and frustrating next-nearest-neighbor exchange couplings J ₁ and J ₂. It is well known that a nonmagnetic phase arises in this model for 0.4 ? J ₂/J ₁ ? 0.6, sandwiched by two Néel ordered phases. In agreement with previous results, we observe a first-order quantum phase transition (QPT) at J ₂ ≈ 0.64 J ₁ from the non-magnetic phase to the Néel one. A large gap (? 0.4J ₁) is found in the singlet spectrum for J ₂ < 0.64J ₁, which excludes a gapless spin-liquid state for 0.4 ? J ₂/J ₁ ? 0.6 and the deconfined quantum criticality scenario for the QPT to another Néel phase. We observe a first-order QPT at J ₂ ≈ 0.55J ₁, presumably between two nonmagnetic phases.     

Bond operator theory for the frustrated anisotropic Heisenberg antiferromagnet on a square lattice

The quantum anisotropic antiferromagnetic Heisenberg model with single ion anisotropy, spin S=1 and up to the next-next-nearest neighbor coupling (the J₁–J₂–J₃ model) on a square lattice, is studied using the bond-operator formalism in a mean field approximation. The quantum phase transitions at zero temperature are obtained. The model features a complex T=0 phase diagram, whose ordering vector is subject to quantum corrections with respect to the classical limit. The phase diagram shows a quantum paramagnetic phase situated among Neél, spiral and collinear states.     

Nonequilibrium phase transition in the kinetic Ising model on a two-layer square lattice under the presence of an oscillating field

The nonequilibrium or dynamic phase transitions are studied, within a mean-field approach, in the kinetic Ising model on a two-layer square lattice consisting of spin- 1/2 ions in the presence of a time varying (sinusoidal) magnetic field has been studied by using Glauber-type stochastic dynamics. The dynamic equations of motion are obtained in terms of the intralayer coupling constants J₁ and J₂ for the first and second layer, respectively, and interlayer coupling constant J₃ between these two layers. The nature (first- or second-order) of the transitions is characterized by investigating the behavior of the thermal variations of the dynamic order parameters. The dynamic phase transitions are obtained and the dynamic phase diagrams are constructed in the plane of the reduced temperature versus the amplitude of the magnetic field and found fourteen fundamental types of phase diagrams. Phase diagrams exhibit one, two or three dynamic tricritical points for various values of J₂/|J₁| and J₃/|J₁|. Besides the paramagnetic (p), ferromagnetic (f) and compensated (c) phases, there were the f+c,f+sf,c+sf,af+p,m+p,f+m and c+af, where the af, sf and m are the antiferromagnetic, surface ferromagnetic and mixed phases respectively. Coexistence phase regions also exist in the system.     

Quantum entanglement and quantum phase transitions in frustrated Majumdar-Ghosh model

By using the density matrix renormalization group technique, the quantum phase transitions in the frustrated Majumdar-Ghosh model are investigated. The behaviors of the conventional order parameter and the quantum entanglement entropy are analyzed in detail. The order parameter is found to peak at J₂∼0.58, but not at the Majumdar-Ghosh point (J₂=0.5). Although, the quantum entanglements calculated with different subsystems display dissimilarly, the extremes of their first derivatives approach to the same critical point. By finite size scaling, this quantum critical point J^C₂ converges to around 0.301 in the thermodynamic limit, which is consistent with those predicted previously by some authors (Tonegawa and Harada, 1987 [6]; Kuboki and Fukuyama, 1987 [7]; Chitra et al., 1995 [9]). Across the J^C₂, the system undergoes a quantum phase transition from a gapless spin-fluid phase to a gapped dimerized phase.     

The temperature-dependent phase diagrams of the spin-3/2 Ising model on a FM/AFM two-layer lattice with a crystal field

The temperature-dependent phase diagrams of the spin-3/2 Ising model on a two-layer Bethe lattice with ferromagnetic (FM)/antiferromagnetic (AFM) intra-layer and either FM or AFM type inter-layer interactions are investigated under a constant magnetic field (H) and in the presence of a crystal field (D) by using exact recursion equations in a pairwise approach for coordination numbers q=3,4 and 6, in detail. In the light of the ground-state (GS) phase diagrams, the temperature-dependent phase diagrams of the model are obtained by studying the thermal variations of the order parameters, response functions and free energy. Then, they are illustrated on the (kT/J₁,J₃/J₁) and (kT/J₁,J₂/J₁) planes for the given system parameters. It is observed that the system exhibits first- and second-order phase transitions for all q values, and hence, in some cases, tricritical points. The existence of critical-end points and that of isolated points are also observed. The re-entrant behavior owes its presence to the two Néel temperatures, T_N, that are present for all q.     

Smeared spin-flop transition in random antiferromagnetic Ising chain

At T = 0 and in a sufficiently large field, the nearest-neighbor antiferromagnetic Ising chain undergoes a first-order spin-flop transition into the ferromagnetic phase. We consider its smearing under the random-bond disorder such that all independent random bonds are antiferromagnetic (AF). It is shown that the ground-state thermodynamics of this random AF chain can be described exactly for an arbitrary distribution P(J) of AF bonds. Moreover, the site magnetizations of finite chains can be found analytically in this model. We consider a continuous P(J) that is zero above some ?J ₁ and behaves near it as (?J ₁?J)^λ, λ > ?1. In this case, the ferromagnetic phase emerges continuously in a field H > H _c = 2J ₁. At 0 > λ > ?1, it has the usual second-order anomalies near H _c with the critical indices obeying the scaling relation and depending on λ. At λ > 0, higher-order transitions occur (third, fourth, etc.), marked by a divergence of the corresponding nonlinear susceptibilities. In the chains with an even number of spins, the intermediate “bow-tie” phase with linearly modulated AF order exists between the AF and ferromagnetic phases at J ₁ < H < H _c . Its origin can be traced to the infinite correlation length of the degenerate AF phase from which it emerges. This implies the existence of similar inhomogeneous phases with size- and form-dependent order in a number of other systems with infinite correlation length. The possibility to observe the signs of the “bow-tie” phase in low-T neutron diffraction experiments is discussed.     

Chiral spin liquid in a two-dimensional helical XY magnet with two chiral order parameters

The critical properties of an XY helimagnet on a square lattice with two chiral order parameters are studied by Monte Carlo simulations. This model is a modification of the J ₁-J ₂-J ₃ model with J ₂ = 0. The case of different third range order interactions J ₃ are considered, J ₃ ^a ?? J ₃ ^b . A first order transition is found away from the Lifshitz points 4J ₃ ^a = J ₁ and 4 J ₃ ^b = J ₁. It is pointed out that a chiral spin liquid phase possibly exists near the Lifshitz points.     

Phase diagram of the Ising antiferromagnet with nearest-neighbor and next-nearest-neighbor interactions on a square lattice

The phase diagram of the Ising model in the presence of nearest-neighbor (J₁) and next-nearest-neighbor (J₂) interactions on a square lattice is studied within the framework of the differential operator technique. The Hamiltonian is solved by effective-field theory in finite cluster (we have chosen N=4 spins). We have proposed a functional for the free energy (similar to Landau expansion) to obtain the phase diagram in the (T,α) space (α=J₂/J₁), where the transition line from the superantiferromagnetic (SAF) to the paramagnetic (P) phase is of first-order in the range 1/2<α<0.95 in contrast to previous study of CVM (Cluster Variational Method) that predict first-order transition for α=1.0. Our results for α=1.0 are in accordance with MC (Monte Carlo) simulations, that predict a second-order transition.     

Phase transitions and critical properties of the frustrated Heisenberg model on a layer triangular lattice with next-to-nearest-neighbor interactions

The critical behavior of the three-dimensional antiferromagnetic Heisenberg model with nearest-neighbor (J) and next-to-nearest-neighbor (J ₁) interactions is studied by the replica Monte Carlo method. The first-order phase transition and pseudouniversal critical behavior of this model are established for a small lattice in the interval R = |J ₁/J| = 0?C0.115. A complete set of the main static magnetic and chiral critical indices is calculated in this interval using the finite-dimensional scaling theory.     

The light pressure force and the friction and diffusion coefficients for atoms in a resonant nonuniformly polarized laser field

The motion of slow atoms with degenerate energy levels in a resonant, nonuniformly polarized laser field is described by the Fokker-Planck equation for the atomic distribution function in phase space in terms of the semiclassical approach. Field gradient expansions are used for the spatially nonuniform coefficients of the equation. For closed atomic transitions J _g =J→J _e =J+1 (J _g and J _e are the total angular momenta of the ground and excited states, respectively), new analytical results are presented for the light pressure force and the friction and diffusion coefficients in momentum space. These results allow the kinetic effects (laser cooling, localization in optical potential wells, etc.) in a field of arbitrary one-, two-, or three-dimensional configuration to be investigated. In several cases, the new contributions to the friction coefficient are interpreted qualitatively.     

Phase diagram of the two-dimensional Ising model with random competing interactions

An Ising model with ferromagnetic nearest-neighbor interactions J₁ (J₁>0) and random next-nearest-neighbor interactions [+J₂ with probability p and −J₂ with probability (1−p); J₂>0] is studied within the framework of an effective-field theory based on the differential-operator technique. The order parameters are calculated, considering finite clusters with n=1,2, and 4 spins, using the standard approximation of neglecting correlations. A phase diagram is obtained in the plane temperature versus p, for the particular case J₁=J₂, showing both superantiferromagnetic (low p) and ferromagnetic (higher values of p) orderings at low temperatures.     

Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpiński gasket

The anisotropic antiferromagnetic Ising model on the fractal Sierpiński gasket is intensively studied, and a number of exotic properties are disclosed. The ground state phase diagram in the plane of magnetic field-interaction of the system is obtained. The thermodynamic properties of the three plateau phases are probed by exploring the temperature-dependence of magnetization, specific heat, susceptibility and spin-spin correlations. No phase transitions are observed in this model. In the absence of a magnetic field, the unusual temperature dependence of the spin correlation length is obtained with 0 ≤ J_b/J_a< 1, and an interesting crossover behavior between different phases at J_b/J_a = 1 is unveiled, whose dynamics can be described by the J_b/J_a-dependence of the specific heat, susceptibility and spin correlation functions. The exotic spin-spin correlation patterns that share the same special rotational symmetry as that of the Sierpiński gasket are obtained in both the 1 / 3 plateau disordered phase and the 5/9 plateau partially ordered ferrimagnetic phase. Moreover, a quantum scheme is formulated to study the thermodynamics of the fractal Sierpiński gasket with Heisenberg interactions. We find that the unusual temperature dependence of the correlation length remains intact in a small quantum fluctuation.     

The transverse spin-1 Ising model with random interactions

The phase diagrams of the transverse spin-1 Ising model with random interactions are investigated using a new technique in the effective field theory that employs a probability distribution within the framework of the single-site cluster theory based on the use of exact Ising spin identities. A model is adopted in which the nearest-neighbor exchange couplings are independent random variables distributed according to the law P(J_ij)=pδ(J_ij−J)+(1−p)δ(J_ij−αJ). General formulae, applicable to lattices with coordination number N, are given. Numerical results are presented for a simple cubic lattice. The possible reentrant phenomenon displayed by the system due to the competitive effects between exchange interactions occurs for the appropriate range of the parameter α.     

Magnetic phase diagram of EuSySe1−y and EuSe under hydrostatic pressure

AC-susceptibility measurements of samples EuS_ySe_1?y and EuSe with applied hydrostatic pressure up to 15 kbar are reported and the magnetic phase diagrams of both systems are compared. Special attention is given to the range where the ferromagnetic and antiferromagnetic exchange interactions just compensate. Whereas in EuSe with applied pressure antiferromagnetic or ferromagnetic ordering is observed up to very close to the critical point J₁=-J₂, a spin glass phase occurs in EuS_ySe_1?y at the corresponding concentration.     

Phase transition of an antiferromagnetic system of triplet ions with uniaxial anisotropy in a parallel magnetic field

Using a molecular field approximation we study the metamagnetic behavior in a magnetic field parallel to the anisotropy axis, of an assembly of pseudo spins (S = 1) with a single ion uniaxial anisotropy (D) of the same order of magnitude as the magnetic exchange couplings. The ions are divided in two sublattices with an intrasublattice ferromagnetic coupling (J₁) and an antiferromagnetic coupling (J₂) between distinct sublattices. We have taken a particular interest in the evolution of the phase diagram with parameters D, J₁ and J₂ and we have developed the study of the nature of the point separating first and second order transition lines. A comparison with experimental situations concerning FeCl₂ and FeBr₂ is given.     

Behaviour at ok and at different magnetic fields of the double magnetic helix

We study the behaviour at 0K and at all magnetic field values up to the magnetic saturation of the magnetic helix in which two distinct magnetic ions of spin lengths S₁, and S₂ are acted on by two unequal molecular fields. Although limited to the case of zigzag and collinear chains on which only the magnetic interactions J between first nearest neighbours (n.n) and J₁, or J₁ between second n.n. are considered, complex phase diagrams are obtained. The most disclosing features show up by taking S₁, S₂, J₁,J₂ as parameters and h, J as variables. Whereas the biconical configuration appears as the most general solution, triangular and oblique configurations also exist in finite field in all (h, J) diagrams. In addition, a collinear ferrimagnetic configuration is found to be stable for definite h and J values. We finally observe that according to the ratio values S₁S₂ and $\text{(J}{}_2\text{J}{}_1\text{)}\text{1}\text{2}$, eight types of (h, J) diagrams exist which differ from each other by distinct approaches to the ferri- or ferromagnetic alignment.     

Physics of the pseudogap phase of high Tc cuprates, or, RVB meets umklapp

It is argued that the dominant feature of the phase diagram of the high T_c cuprates is the crossover to the pseudogap phase in the energy (temperature) region E(T^∗). We argue that this scale is determined by the effective anti-ferromagnetic interaction which we calculate to be J_eff=J_{superexchange}−xt where x is the hole percentage and t the hopping integral.