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.     

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.     

Modulated Phase of a Potts Model with Competing Binary Interactions on a Cayley Tree

We study the phase diagram for Potts model on a Cayley tree with competing nearest-neighbor interactions J ₁, prolonged next-nearest-neighbor interactions J _p and one-level next-nearest-neighbor interactions J _o . Vannimenus proved that the phase diagram of Ising model with J _o =0 contains a modulated phase, as found for similar models on periodic lattices, but the multicritical Lifshitz point is at zero temperature. Later Mariz et al. generalized this result for Ising model with J _o ≠0 and recently Ganikhodjaev et al. proved similar result for the three-state Potts model with J _o =0. We consider Potts model with J _o ≠0 and show that for some values of J _o the multicritical Lifshitz point be at non-zero temperature. We also prove that as soon as the same-level interactionJ _o is nonzero, the paramagnetic phase found at high temperatures for J _o =0 disappears, while Ising model does not obtain such property. 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 by Ganikhodjaev et al. for J _o =0. At vanishing temperature, the phase diagram is fully determined for all values and signs of J ₁,J _p and J _o . At finite temperatures several interesting features are exhibited for typical values of J _o /J ₁.     

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.     

Phase transition in Ising, XY and Heisenberg magnetic films

The phase transition and magnetic properties of a ferromagnet spin-S, a disordered diluted thin and semi-infinite film with a face-centered cubic lattice are investigated using the high-temperature series expansions technique extrapolated with Padé approximants method for Heisenberg, XY and Ising models. The reduced critical temperature of the system τ_c is studied as function of the thickness of the thin film and the exchange interactions in the bulk, and within the surfaces J_b, J_s and J_⊥, respectively. It is found that τ_c increases with the exchange interactions of surface. The magnetic phase diagrams (τ_c versus the dilution x) and the percolation threshold are obtained. The shifts of the critical temperatures T_c(l) from the bulk value (T_c(∞)/T_c(l) − 1) can be described by a power law l^−λ, where λ = 1/υ is the inverse of the correlation length exponent.     

Mixed spin- and spin- Ising models with random nearest-neighbour interactions

Using the effective field theory with correlations, we study mixed spin?3/2 and spin?1/2 Ising models with random bonds and crystal-field interactions on the honeycomb lattice. The nearest-neighbour couplings J_ij are taken as random variables with distribution P(J_ij) = pδ(J_ij ? J)+(1 ? p)δ(J_ij ? αJ), where J > 0 and |α| ≤ 1. In a certain range of negative values of α, the phase diagrams exhibit re-entrant behaviour. In detail, we investigate separately two kinds of disorder: Bond dilution (α = 0) and random ±J interactions (α = ?1). In both cases, the influence of the an-isotropy on the phase diagrams shows some new outstanding features.     

The mixed-spin ternary-alloy in the form of ABpC1−p on the Bethe lattice

The AB_pC_1−p type of mixed ferromagnetic-ferrimagnetic ternary-alloy with A (spin-3/2), B (spin-1) and C (spin-5/2) ions was studied on the Bethe lattice with the odd numbered shells containing only A ions, while the even numbered shells either containing B or C ions randomly. The phase diagrams were obtained on the (R=|J_AC|/J_AB,kT_c/J_AB) and (p, kT_c/J_AB) planes for given values of p and R, respectively, with the coordination numbers z=3, 4, 5 and 6. The explicit dependence of the phase diagrams on z and each shell of the Bethe lattice having only one type of ion lead to some differences when compared with the previous works. The model presents one or two compensation temperatures for appropriate values of the system parameters.     

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.     

Dynamic phase transitions in the kinetic spin-1 Blume-Capel model on the Bethe lattice

The stationary states of the kinetic spin-1 Blume-Capel (BC) model on the Bethe lattice are analyzed in detail in terms of recursion relations. The model is described using a Glauber-type stochastic dynamics in the presence of a time-dependent oscillating external magnetic field (h) and crystal field (D) interactions. The dynamic order parameter, the hysteresis loop area and the dynamic correlation are calculated. It is found that the magnetization oscillates around nonzero values at low temperatures (T) for the ferromagnetic (F) phase while it only oscillates around zero values at high temperatures for the paramagnetic (P) phase. There are regions of the phase space where the two solutions coexist. The dynamic phase diagrams are obtained on the (kT/J,h/J) and (kT/J,D/J) planes for the coordination number q=4. In addition to second-order and first-order phase transitions, dynamical tricritical points and triple points are also observed.     

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.     

Phase diagrams of a nonequilibrium mixed spin-3/2 and spin-2 Ising system in an oscillating magnetic field

The phase diagrams of the nonequilibrium mixed spin-3/2 and spin-2 Ising ferrimagnetic system on square lattice under a time-dependent external magnetic field are presented by using the Glauber-type stochastic dynamics. The model system consists of two interpenetrating sublattices of spins σ=3/2 and S=2, and we take only nearest-neighbor interactions between pairs of spins. The system is in contact with a heat bath at absolute temperature T_abs and the exchange of energy with the heat bath occurs via one-spin flip of the Glauber dynamics. First, we investigate the time variations of average order parameters to find the phases in the system and then the thermal behavior of the dynamic order parameters to obtain the dynamic phase transition (DPT) points as well as to characterize the nature (first- or second-order) phase transitions. The dynamic phase diagrams are presented in two different planes. Phase diagrams contain paramagnetic (p), ferrimagnetic (i₁, i₂, i₃) phases, and three coexistence or mixed phase regions, namely i₁+p, i₂+p and i₃+p mixed phases that strongly depend on interaction parameters.     

Dynamic phase transitions and dynamic phase diagrams of the Blume–Emery–Griffiths model in an oscillating field: the effective-field theory based on the Glauber-type stochastic dynamics

Using the effective-field theory based on the Glauber-type stochastic dynamics (DEFT), we investigate dynamic phase transitions and dynamic phase diagrams of the Blume–Emery–Griffiths model under an oscillating magnetic field. We presented the dynamic phase diagrams in (T/J, h₀/J), (D/J, T/J) and (K/J, T/J) planes, where T, h₀, D, K and z are the temperature, magnetic field amplitude, crystal–field interaction, biquadratic interaction and the coordination number. The dynamic phase diagrams exhibit several ordered phases, coexistence phase regions and special critical points, as well as re-entrant behavior depending on interaction parameters. We also compare and discuss the results with the results of the same system within the mean-field theory based on the Glauber-type stochastic dynamics and find that some of the dynamic first-order phase lines and special dynamic critical points disappeared in the DEFT calculation.     

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.     

15N(p,po)15N and the levels of 16O for Ex = 14.8–18.6 MeV

Angular distributions of cross section and analyzing power for elastic scattering of protons from ¹⁵N have been measured for E_p = 2.7–7.0 MeV. A phase-shift analysis of the data yields spin-parity assignments and level parameters for seventeen states of ¹⁶O in the excitation energy region 14.8–18.6MeV. Three of the resonances have not previously been identified, among them being a broad J^π = 2^? level at E_p = 6.1 MeV which is almost certainly the analog of the 2^? 1p1h state with configuration ($\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{,}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$) at E_x ∽ 5.0 MeV in ¹⁶N. The broad level previously reported near E_p = 5.0 MeV has been observed and its parameters determined. A resonance analysis of the phase shifts yielded values of E_r, Γ and Γ_p for all of the levels. The J^π assignments are in agreement with previously reported values. For resonances having J = l, the data can usually be fit with a resonant phase shift corresponding to either J = l + 1 or J = l ? 1, in addition to the phase shift for J = l. Which of the two spurious-J solutions occurs seems to depend on whether the partial wave through which the resonant state is formed is $\text{J = l +}\text{1}\text{2}\text{or}\text{J = l ?}\text{1}\text{2}$.     

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 properties of the mixed spin-5/2 and spin-3/2 Blume-Capel Ising system on the two-fold Cayley tree

We use exact recursion relations to study the magnetic properties of the half-integer mixed spin-5/2 and spin-3/2 Blume-Capel Ising ferromagnetic system on the two-fold Cayley tree that consists of two sublattices A and B. Two positive crystal-field interactions Δ₁ and Δ₂ are considered for the sublattice with spin-5/2 and spin-3/2 respectively. For different coordination numbers q of the Cayley tree sites, the phase diagrams of the model are presented with a special emphasis on the case q = 3, since other values of q reproduce similar results. First, the T = 0 phase diagram is illustrated in the (D _A = Δ₁/J,D _B = Δ₂/J) plane of reduced crystal-field interactions. This diagram shows triple points and coexistence lines between thermodynamically stable phases. Secondly, the thermal variation of the magnetization belonging to each sublattice for some coordination numbers q are investigated as well as the Helmoltz free energy of the system. First-order and second-order phase transitions are found. The second-order phase transitions become sharper and sharper when D _A or D _B increases. The first-order transitions only exist for some appropriate non-zero values of D _A and/or D _B . The corresponding transition lines never connect to the second-order transition lines. Thus, the non-existence of tricritical points remains one of the key features of the present model. The magnetic exponent β ₀ of the model is estimated and found to be ¼ at small values of D _A = D _B = D and β ₀ = ½ at large values of D. At intermediate values of D, there is a crossover region where the magnetic exponent displays interesting behaviours.     

Frustrated model to describe reentrant behavior in copper oxide superconductors

The quenched decorated Ising model with competitive interactions is used here to described the magnetic properties of the copper oxide superconductors compounds in the insulating phase (antiferromagnetic). The model consists of planes in which the nodal spins interact antiferromagnetically (J_A<0) with their nearest-neighbors, and ferromagnetically (J_F>0) with the spins that decorate the bonds, which are quenched and distributed randomly over the two-dimensional lattice. The planes interact antiferromagnetically with weak-exchange interaction (i.e., , λ=10^-5). By using the framework of an effective-field theory, based on the differential operator technique, we discuss the antiferromagnetic-phase stability limit in the temperature-decorated bond concentration space (T-p), for λ=10^-5 and various values of frustration parameter α=J_A/J_F. For certain region range of the parameter α we observe a reentrant behavior at low-temperature. We also discuss the critical behavior of T_N versus α for some values of decorated bond concentrations and reentrant phenomena is observed. We calculate the dependence of the staggered magnetization as a function of the temperature to analyze the reentrant behavior observed in the phase diagrams.     

The Rotational Spectrum of SiHF3 in the Vibrational State υ6=2: Observation of Direct l-Type Resonance Transitions

The υ₆=2 vibrational state of the main isotopomer of trifluorosilane, ²⁸SiHF₃, has been investigated in the centimeter- and millimeter-wave ranges. Rotational spectra following the Δ J=1, Δk=Δ l=0 selection rule have been measured up to J=24 and K=23 and for both values of ∣l∣. Two types of direct l-type resonance transitions induced by the (Δ l=Δk=±2) interaction could be observed by means of waveguide Fourier transform microwave spectroscopy in the range 8-26 GHz: 252 transitions following the Δ J=0, Δl=Δk=±2 selection rule covering values of J=7-39 and G=∣k-l∣ from 1 to 18 and 90 transitions following the Δ J=0, Δl=Δ k=±4 selection rule covering values of J=17-52 and G from 1 to 4. Due to the strong (2,2) resonance, 18 A₁-A₂ splittings of the k=l=±2 states from J=36-53 could also be observed. Accidental near-degeneracies lead to strong perturbations due to Δ (k-l)=±3 interactions, enabling the observation of perturbation-allowed transitions with selection rules k=±3(l=±2)↔±4(±2), ±2(±2), A₊↔ ±1(?2), A₋ and ± 1(0)↔± 6(±2). In a multiple-fit analysis the experimental data have been refined using five reduced forms of the effective Hamiltonian as proposed by Sarka and Harder [J. Mol. Spectrosc.197, 254-261 (1999)]. Parameters up to seventh order have been determined including the axial rotational constant C for both values of ∣l∣ and the vibrational separation of the ∣l∣=0 and 2 states. The unitary equivalence of the determined parameter sets has been demonstrated up to fifth order. Differences of the rotational constants in the various parameter sets have been explained by the theory of reduction. Sign relations of the fitted parameters and general features of the direct l-type resonance spectrum in a υ_t=2 level are discussed.     

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

We have used the real-space Migdal-Kadanoff renormalization group technique on d-dimensional hypercubic lattice to study the mixed spin-1/2 and spin-2 Blume-Capel model. First, we indicate a critical dimension d_C ≈?2.05, above and below which different topologies of phase diagrams occur. The phase diagrams have been plotted in the (crystal field, temperature) plane around d_C, in which there is a second-order phase transition. Moreover, using the variation of the free energy at low temperatures, we have established the ground-state phase diagrams in the (?/J, C/J) plane for d?<?d_C and d?≥?d_C. In particular, we have seen the appearance of two first-order transitions at very low temperatures by the use of the free energy and its isotherm derivative. A detailed analysis of fixed points and flow diagrams indicates that there is no tricritical point.

     

Spin Dynamics and Dirac Nodes in a Kagome Lattice

Herein, the spin dynamics for various magnetic configurations arranged on a Kagome lattice is investigated. Using a Holstein–Primakoff expansion of the isotropic Heisenberg Hamiltonian with multiple exchange parameters, the development and evolution of magnetic Dirac nodes with both anisotropy and magnetic field are examined. From the classical energies, the phase diagrams for the ferromagnetic (FM), antiferrimagnetic (AfM), and the 120°  phases are shown as functions of J₁, J₂, J₃, and anisotropy. Furthermore, the production of bosonic Dirac and Weyl nodes in the spin-wave spectra is shown. Through frustration of the magnetic geometry, a connection to the asymmetric properties of the Kagome lattice and the various antiferromagnetic configurations is discerned. Most interesting is the 120°  phase, which does not have Dirac nodes when considering only J₁ due to the formation of an analogous antiferromagnetic honeycomb lattice, but gains Dirac symmetry with next-nearest neighbor interactions. Additionally, the presence of flat modes that are characteristic of cluster excitations is shown. Further study of external frustrations from a magnetic field and anisotropy reveals a tunability of the exchange interactions and nodal points.