The Bethe lattice treatment of sound attenuation for a spin- 3/2 Ising model

The sound attenuation phenomena is investigated for a spin- 3/2 Ising model on the Bethe lattice in terms of the recursion relations by using the Onsager theory of irreversible thermodynamics. The dependencies of sound attenuation on the temperature (T$T$), frequency (w$w$), Onsager coefficient (γ$\gamma$) and external magnetic field (H$H$) near the second-order (_Tc)$\left(T_c\right)$ and first-order (_Tt)$\left(T_t\right)$ phase transition temperatures are examined for given coordination numbers q$q$ on the Bethe lattice. It is assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process, thus two relaxation times are obtained and which are used to obtain an expression for the sound attenuation coefficient (α)$\left(\alpha \right)$. Our investigations revealed that only one peak is obtained near _Tt$T_t$ and three peaks are found near _Tc$T_c$ when the Onsager coefficient is varied at a given constant frequency for q=3$q=3$. Fixing the Onsager coefficient and varying the frequency always leads to two peaks for q=3,4$q=3,4$ and 6 near _Tc$T_c$. The sound attenuation peaks are observed near _Tt$T_t$ at lower values of external magnetic field, but as it increases the sound attenuation peaks decrease and eventually disappear.     

Critical properties of mixed spin-1 and spin-5/2 with equal and unequal crystal fields

The effects of assuming equal or unequal crystal fields (CF) on the phase diagrams of a mixed spin-1 and spin-5/2 system are investigated in terms of the recursion relations on the Bethe lattice (BL). The equal CF case was considered for the coordination numbers q=3, 4, and 6, while for q=3 the unequal CF case was also studied. It was found that for the equal CF case, the model exhibits second-order phase transitions and two compensation temperatures for all q, the reentrant behavior for q=4 and first-order phase transitions and tricritical point (TCP) for q=6. In the unequal CF case for q=3, the system yields first- and second-order phase transitions, TCP's, and three compensation temperatures. In addition, the TCP's in a very short range are classified as the stable and unstable ones depending on their free energies.     

Thermal entanglement in two-qutrit spin-1 anisotropic Heisenberg model with inhomogeneous magnetic field

The thermal entanglement of a two-qutrit spin-1 anisotropic Heisenberg XXZ chain in an inhomogeneous magnetic field is studied in detail. The effects of the external magnetic field (B), a parameter b which controls the inhomogeneity of B, and the bilinear interaction parameters J_{x=Jy≠Jz on the thermal variation of the negativity are studied in detail. It is found that negativity N decreases when the values of magnetic field, inhomogeneity b and temperature are increasing. In addition, N remains at higher temperatures for higher values of Jz and lower values of B and b.}     

An exact formulation of the Blume-Emery-Griffiths model on a two-fold Cayley tree model

A two-fold Cayley tree graph with fully q-coordinated sites is constructed and the spin-1 Ising Blume-Emery-Griffiths model on the constructed graph is solved exactly using the exact recursion equations for the coordination number q = 3. The exact phase diagrams in (kT/J, K/J ) and (kT/J, D/J) planes are obtained for various values of constants D/J and K/J, respectively, and the tricritical behavior is found. It is observed that when the negative biquadratic exchange (K) and the positive crystal-field (D) interactions are large enough, the tricritical point disappears in the (kT/J, K/J) plane. On the other hand, the system always exhibits a tricritical behavior in the phase diagram of (kT/J, D/J) plane. Received 8 June 2001 and Received in final form 28 September 2001     

Isothermal Entropy Change for the Spin-1 Blume-Capel Model on the Bethe Lattice

The isothermal entropy change of spin-1 Blume-Capel (BC) is investigated on the Bethe lattice (BL) with the variations of coordination numbers (q), crystal field (D) and external magnetic field (H) in the vicinity of critical temperatures, i.e. about the second- and first-order phase transition temperatures. The calculation is carried on the BL in terms of exact recursion relations. It is found that the peaks of the isothermal entropy variation obtained for both magnetization and quadrupole moments are observed to be increasing with increasing values of H for given D and q, decreasing with the increasing q for fixed D and H and also decreasing with the increasing values of D for constant q and H. The peaks of the curves for the quadrupole moment is less sharper then the ones obtained for the magnetization.

     

The question of equivalence for generalized Hausdorff matrices

In the present paper we investigate when Hausdorff matrices and generalized Hausdorff matrices, with the same mass function, are equivalent, as bounded operators on c and ?p.     

Molecular Structure and Supramolecular Architecture of (E)-2-Bromo-6-[(2,4,6-Tribromophenylimino)methyl]-4-Chlorophenol

Crystallography Reports - In this study, the molecular structure and supramolecular architecture of a new compound have been studied in depth using single crystal X-ray diffraction (XRD) technique....     

(<Emphasis Type="Italic">E</Emphasis>)-2-[(2-Bromophenylimino)methyl]-5-methoxyphenol: X-ray and DFT-calculated structures

The crystal structure of (E)-2-[(2-Bromophenylimino)methyl]-5-methoxyphenol is determined by using X-ray diffraction and then the molecular structure is investigated with density functional theory (DFT). X-Ray study shows that the title compound has a strong intramolecular O-H…N hydrogen bond and three dimensional crystal structure is primarily determined by C-H…π and weak van der Waals interactions. The strong O-H…N bond is an evidence of the preference for the phenol-imine tautomeric form in the solid state. Optimized molecular geometry is calculated with DFT at the B3LYP/6-31G(d,p) level. The IR spectra of compound were recorded experimentally and calculated to compare with each other. The results from both experiment and theoretical calculations are compared in this study.     

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.