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 statistical mechanics of spin-1 Ising model with AFM/AFM interactions on a bilayer Bethe lattice

The spin-1 Ising model is studied for the case of antiferromagnetic (AFM)/AFM interactions on the bilayer Bethe lattice by using the pairwise approach for several values of the coordination numbers q=3, 4 and 6 when the layers are linked with the external magnetic fields. The ground state (GS) phase diagrams, thermal variations of the order-parameters and the response functions are studied in detail to obtain the phase diagrams of the model. It was found that the system gives only one Néel temperature, T_N, for q=3. Two T_N's and first-order phase transition temperature, T_t, thus tricritical point, are found and the existence of two T_N's leads to the reentrant behavior when q=4 and 6 for some given system parameters.     

Spin-3/2 Ising model AFM/AFM two-layer lattice with crystal field

The spin-3/2 Ising model is investigated for the case of antiferromagnetic (AFM/AFM) interactions on the two-layer Bethe lattice by using the exact recursion relations in the pairwise approach for given coordination numbers q=3, 4 and 6 when the layers are under the influences of equal external magnetic and equal crystal fields. The ground state (GS) phase diagrams are obtained on the different planes in detail and then the temperature-dependent phase diagrams of the system are calculated accordingly. It is observed that the system presents both second- and first-order phase transitions for all q, therefore, tricritical points. It is also found that the system exhibits double-critical end points and isolated points. The model also presents two Néel temperatures, T_N, and the existence of which leads to the reentrant behaviour.     

The spin-1 Ising model on a two-layer Bethe lattice with FM/AFM interactions

Two-layer Bethe lattice with the Ising spins of the top layer having only ferromagnetic (FM) interactions and the bottom layer having only antiferromagnetic (AFM) interactions are allowed to interact with the interlayer interaction of either FM or AFM type. The model is studied by using the exact recursion relations in a pairwise approach for given coordination numbers q=3, 4 and 6 with equal external magnetic fields acting on the layers. The phase diagrams of the model are obtained on different planes for given system parameters by studying the ground state (GS) phase diagrams and the thermal variations of the order-parameters and the response functions, i.e. the susceptibility and the specific heat, in detail. The model presents second- and first-order phase transitions, and where their lines are combined is the tricritical point. The critical end points also exist. The reentrant behavior is also seen when the model presents two Néel temperatures.     

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.     

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.     

Magnetic ordering in CeMnCuSi2

Temperature and field-dependent magnetization measurements on polycrystalline CeMnCuSi₂ reveal that the Mn moments in this compound exhibit ordering with a ferromagnetic (FM) component ordered instead of the previously reported purely antiferromagnetic (AFM) ordering. The FM ordering temperature, T_c, is about 120 K and almost unchanged with external fields up to 50 kOe. Furthermore, an AFM component (such as in a canted spin structure) is observed to be present in this phase, and its orientation is modified rapidly by the external magnetic field. The Ce L₃-edge X-ray absorption result shows that the Ce ions in this compound are nearly trivalent, very similar to that in the heavy fermion system CeCu₂Si₂. Large thermomagnetic irreversibility is observed between the zero-field-cooled (ZFC) and field-cooled (FC) M(T) curves below T_c indicating strong magnetocrystalline anisotropy in the ordered phase. At 5 K, a metamagnetic-type transition is observed to occur at a critical field of about 8 kOe, and this critical field decreases with increasing temperature. The FM ordering of the Mn moments in CeMnCuSi₂ is consistent with the value of the intralayer Mn–Mn distance R^a_Mn–Mn=2.890 Å, which is greater than the critical value 2.865 Å for FM ordering. Finally, a magnetic phase diagram is constructed for CeMnCuSi₂.     

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.     

Charge order melting and magnetic transition in Nd0.5(1+x)Ca0.5(1−x)Mn(1−x)CrxO3 system

The magnetic property of double doped manganite Nd_0.5(1+x)Ca_0.5(1−x)Mn_(1−x)Cr_xO₃ with a fixed ratio of Mn³⁺:Mn⁴⁺=1:1 has been investigated. For the undoped sample, it undergoes one transition from charge disordering to charge ordering (CO) associated with paramagnetic (PM)-antiferromagnetic (AFM) phase transition at T<250 K. The long range AFM ordering seems to form at 35 K, rather than previously reported 150 K. At low temperature, an asymmetrical M-H hysteresis loop occurs due to weak AFM coupling. For the doped samples, the substitution of Cr³⁺ for Mn³⁺ ions causes the increase of magnetization and the rise of T_c. As the Cr³⁺ concentration increases, the CO domain gradually becomes smaller and the CO melting process emerges. At low temperature, the FM superexchange interaction between Mn³⁺ and Cr³⁺ ions causes a magnetic upturn, namely, the second FM phase transition.     

The crystal-field dependency of sound attenuation in the spin-3/2 ising model

The effects of crystal-field (D) on sound attenuation are considered for the spin-3/2 Ising model by using Onsager theory of irreversible thermodynamics. It is assumed that the sound wave couples to the order-parameter fluctuations, therefore, it decays mainly via order-parameter relaxation process. The order-parameters, magnetization and quadrupole moment, are defined in terms of exact recursion relations (ERR) on Bethe lattice (BL). After our analysis, two relaxation times are obtained and they are used to calculate the sound attenuation coefficient (α). Consequently, the critical behaviors of sound attenuation coefficient are investigated in terms of frequency (w) and Onsager coefficient (γ) for the coordination numbers q=3, 4 ad 6 near the second-order (T_c) and first-order (T_t) phase transition temperatures in the ferromagnetic phase regions for the negative and positive D values and the results are presented on the (k_BT/J, α) planes. It is found that the peaks about T_t’s are observed at the same temperature, but the peaks about T_c’s are observed shifted to lower and higher temperatures in increasing (w)’s and (γ)’s, respectively. In addition, the peaks are also obtained near the tricritical points for all q.     

Peculiarities of the magnetic,galvanomagnetic, elastic,and magnetoelastic properties of Sm<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Sr<Subscript>x</Subscript>MnO<Subscript>3</Subscript> manganites

Manganites of the Sm1?xSr_xMnO₃ system (x=0.33, 0.4, and 0.45) possess giant negative values of the magnetoresistance Δρ/ρ and the volume magnetostriction ω near the Curie temperature T_C. In the compound with x=0.33, the isotherms of Δρ/ρ, ω, and magnetization σ exhibit smooth variation and do not reach saturation up to maximum magnetic field strengths (120 kOe) studied (according to the neutron diffraction data, this substance comprises a ferromagnetic (FM) matrix with distributed clusters of a layered antiferromagnetic (AFM) structure of the A type). In the compounds with x=0.4 and 0.45 containing, besides the FM matrix and A-type AFM phase, a charge-ordered AFM phase of the CE type (thermally stable to higher temperatures as compared to the A-type AFM and the FM phases), the same isotherms measured at T ≥ T_C show a jumplike increase in the interval of field strengths between H_c1 and H_c2 and then reach saturation. In the interval H_c1 > H > H_c2, the σ, ω, and Δρ/ρ values exhibit a metastable behavior. At temperatures above T_C, the anisotropic magnetostriction changes sign, which is indicative of rearrangements in the crystal structure. The giant values of ω and Δρ/ρ observed at T ≥ T_C for all compounds, together with excess (relative to the linear) thermal expansion and a maximum on the ρ(T) curve, are explained by the phenomenon of electron phase separation caused by a strong s-d exchange. The giant values of magnetoresistance and volume magnetostriction (with ω reaching ～10^?3) are attributed to an increase in the volume of the FM phase induced by the applied magnetic field. In the compound with x=0.33, this increase proceeds smoothly as the FM phase grows through the FM layers in the A-type AFM phase. In the compounds with x=0.4 and 0.45, the FM phase volume increases at the expense of the charge-ordered CE-type AFM structure (in which spins of the neighboring manganese ions possess an AFM order). The jumps observed on the σ(H) curves, whereby the magnetization σ reaches ～70% of the value at T=1.5 K, are indicative of a threshold character of the charge-ordered phase transition to the FM state. Thus, the giant values of ω and Δρ/ρ are inherent in the FM state, appearing as a result of the magnetic-field-induced transition of the charge-ordered phase to the FM state, rather than being caused by melting of this phase.     

Fine structure of the field-induced magnetic transition in Nd0.1La0.9Fe11.5Al1.5

For the Nd_0.1La_0.9Fe_11.5Al_1.5 compound, the fine structure of the magnetic transition from the ferromagnetic (FM) to the antiferromagnetic (AFM) states has been studied carefully by means of magnetization (M) and heat capacity (C_p) measurements. Although a single phase with the cubic NaZn₁₃-type structure (Fm3c) has been proved by the room temperature X-ray diffraction pattern, the phase transition has been clearly found to be a stepwise process in M(T) and C_p(T) curves under proper fields. Due to the strong competition between the FM order and AFM order, the characteristic is especially evident under low fields, weakens gradually with the increasing applied field and finally vanishes when the field is higher than 2 T. This multi-step magnetic transition results from the inhomogeneity of the sample, probably due to the inhomogeneous distribution of Nd atoms.     

The exchange bias and coercivity of FM/AFM films: Monte Carlo simulation

The exchange bias (H_E) and coercivity (H_C) of the ferromagnet/antiferromagnet (FM/AFM) films have been simulated with Monte Carlo method. The simulated results indicate that, the value of H_E decreases with increasing temperature, and the values of H_E and the blocking temperature T_b at which H_E=0 reduce evidently with decreasing absolute value of interlayer exchange coupling JI. It also is found that for the large absolute values of JI, the maximum in H_C occurs very close to T_b. At the same time, it is observed that the diluted ratio of FM at FM/AFM interface influences clearly the value of H_E. The simulated results are consistent with the experimental facts. The maximum behaviour in the H_C−T curves has been explained by the interplay of the softening of some fraction of the spins in the AFM layer near T_N′ and the disorder of the spins in FM layer near Curie temperature T_C.     

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.     

Kinetics of a mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model

We present a study, within a mean-field approach, of the kinetics of a mixed ferrimagnetic model on a square lattice in which two interpenetrating square sublattices have spins that can take two values, , alternated with spins that can take the four values, . We use the Glauber-type stochastic dynamics to describe the time evolution of the system with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field. The nature (continuous and discontinuous) of transition is characterized by studying the thermal behaviors of average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude (h) and reduced temperature (T) plane, and in the reduced temperature and interaction parameter planes, namely in the (h, T) and (d, T) planes, d is the reduced crystal-field interaction. The phase diagrams always exhibit a tricritical point in (h, T) plane, but do not exhibit in the (d, T) plane for low values of h. The dynamic multicritical point or dynamic critical end point exist in the (d, T) plane for low values of h. Moreover, phase diagrams contain paramagnetic (p), ferromagnetic (f), ferrimagnetic (i) phases, two coexistence or mixed phase regions, (f+p) and (i+p), that strongly depend on interaction parameters.     

The effective-field theory studies of critical phenomena in a mixed spin-1 and spin-2 Ising model on honeycomb and square lattices

An effective-field theory with correlations has been used to study critical behaviors of a mixed spin-1 and spin-2 Ising system on a honeycomb and square lattices in the absence and presence of a longitudinal magnetic field. The ground-state phase diagram of the model is obtained in the longitudinal magnetic field (h) and a single-ion potential or crystal-field interaction (Δ) plane. The thermal behavior of the sublattice magnetizations of the system are investigated to characterize the nature of (continuous and discontinuous) of the phase transitions and obtain the phase transition temperature. The phase diagrams are presented in the (Δ/|J|, k_BT/|J|) plane. The susceptibility, internal energy and specific heat of the system are numerically examined and some interesting phenomena in these quantities are found due to the absence and presence of the applied longitudinal magnetic field. Moreover, the system undergoes second- and first-order phase transition; hence, the system gives a tricritical point. The system also exhibits reentrant behavior.     

Josephson current in superconductor/ferromagnet/superconductor junctions

By using the Bogoliubov–de Gennes equation and the Nambu spinor Greens function approach, we have theoretically studied the dc Josephson current and the coupling phase state of superconductor/ferromagnet/superconductor (SC/FM/SC) junctions, where the FM is of weak ferromagnetism. From the behavior of the temperature-dependent dc Josephson current (I_c), we confirm that such SC/FM/SC junction may change from 0-phase to π-phase state with increasing the temperature (T), for particular parameters of the thickness and the strength of ferromagnetism of the FM interlayer. We attribute such changement to an extra phase difference between the two SCs. The results are qualitatively consistent with an experiment [Phys. Rev. Lett. 86 (2001) 2427], which shows a sharp cusp structure on the I_c−T curves of Nb/Cu_0.48Ni_0.52/Nb junction for specific thickness of the Cu_0.48Ni_0.52, indicating the junction changes from 0-phase state at high temperatures to π-phase state at low temperatures.     

Magnetic phase transitions of antiperovskite Mn3−xFexSnC (0.5≤x≤1.3)

The magnetization and electrical resistivity of Mn_3−xFe_xSnC (0.5≤x≤1.3) were measured to investigate the behavior of the complicated magnetic phase transitions and electronic transport properties from 5 to 300 K. The results obtained demonstrate that Fe doping at the Mn sites of Mn₃SnC induces a more complicated magnetic phase transition than that in its parent phase Mn₃SnC from a paramagnetic (PM) state to a ferrimagnetic (FI) state consisting of antiferromagnetic (AFM) and ferromagnetic (FM) components, while, with the change of Fe-doped content and magnetic field, there is a competition between the AFM component and FM component in the FI state. Both the Curie temperature (T_C) and the saturated magnetization M_s increase with increasing x. The FM component region becomes broader with further increasing Fe-doped content x. The external magnetic field easily creates a saturated FM state (and increased T_C) when . Fe doping quenches the negative thermal expansion (NTE) behavior from 200 to 250 K reported in Mn₃SnC.     

Scaling function for order-parameter correlations in expansion to order 1/n: I. Short-range interactions

The order-parameter correlation function $\text{G}\text{?}\text{(}\text{q}\text{, ξ}{}_1\text{)}$ is calculated in the critical region of momentum space $\text{q}$ in terms of a second-moment correlation length ξ₁ by means of perturbation expansion to order 1/n, for an n-vector system with short-range interactions, in zero field above T_c, for 2 < d < 4. The scaling function of the $\text{q}$ dependence is obtained in closed form with a precisely identified cutoff-dependent factor which is the amplitude of the correlation-length dependence of the susceptibility. Both the exponents and the coefficients of the expansion for fixed q as t = (T?T_c)/T_c → 0 are given explicitly and the former are shown to be in accordance with the operator product expansion. The coefficients of order 1/n in the terms associated with a t^k(1?α) dependence of the energy density, for integer k ≥ 1, are expected to be explicitly cutoff-dependent and this is verified by the detailed calculations for k = 1. The behaviour for fixed t and q → 0 is shown to be markedly different from the Ornstein-Zernike approximation. Detailed comparison is provided with the scaling function of the t dependence of the correlations appearing in parallel work.     

Hadron structure in the ladder model (II)

The (flavor non-singlet) probability Φ(k) to find a far-off-shell quark in a hadron is obtained in the renormalization group improved ladder model for QCD in the space-like axial gauge in the region k_T²??2k·P, extending an earlier result for the region k_T²≈?2k·P. The resulting Drell-Yan cross section at measured Q_T agrees in the appropriate limit with that given by Parisi and Petronzio (and disagrees with the DDT form). By using a soft photon method in an abelian gauge theory, I argue that ladder diagrams with strong ordering of gluon q· P's in fact dominate Φ(k) in the high-energy limit considered.