d = 3 anisotropic and d = 2 tJ models: phase diagrams, thermodynamic properties, and chemical potential shift

The anisotropic d=3 tJ model is studied by renormalization-group theory, yielding the evolution of the system as interplane coupling is varied from the isotropic three-dimensional to quasi-two-dimensional regimes. Finite-temperature phase diagrams, chemical potential shifts, and in-plane and interplane kinetic energies and antiferromagnetic correlations are calculated for the entire range of electron densities. We find that the novel τ phase, seen in earlier studies of the isotropic d=3 tJ model, persists even for strong anisotropy. While the τ phase appears at low temperatures at 30–35% hole doping away from 〈 n_i〉=1, at smaller hole dopings we see a complex lamellar structure of antiferromagnetic and disordered regions, with a suppressed chemical potential shift, a possible marker of incommensurate ordering in the form of microscopic stripes. An investigation of the renormalization-group flows for the isotropic two-dimensional tJ model also shows a clear pre-signature of the τ phase, which in fact appears with finite transition temperatures upon addition of the smallest interplane coupling.     

What can we learn from hydrodynamic analysis at RHIC?

We can establish a new picture, the perfect fluid sQGP core and the dissipative hadronic corona, of the space-time evolution of produced matter in relativistic heavy-ion collisions at RHIC. It is also shown that the picture works well also in the forward rapidity region through an analysis based on a new class of the hydro-kinetic model and that this is a manifestation of the rapid increase of the entropy density in the vicinity of QCD critical temperature, namely, deconfinement.     

Jordan-Wigner approach to the frustrated spin one-half XXZ chain

The Jordan-Wigner transformation is applied to study the ground state properties and dimerization transition in the J₁-J₂ XXZ chain. We consider different solutions of the mean-field approximation for the transformed Hamiltonian. Ground state energy and the static structure factor are compared with complementary exact diagonalization and good agreement is found near the limit of the Majumdar-Ghosh model. Furthermore, the ground state phase diagram is discussed within the mean-field theory. In particular, we show that an incommensurate ground state is absent for large J₂ in a fully self-consistent mean-field analysis.     

Statistical verification of crystallization in hard sphere packings under densification

The performance of various structure characteristics in the task of indicating structural peculiarities in packings of hard spheres is investigated. Various characteristics based on Voronoi polyhedra, spherical harmonics, and Delaunay simplices are considered together with the pair correlation function and the mean number of r-close triples. They are applied to a set of hard sphere packings of density φ from 0.62 to 0.72. It turns out that all used structure characteristics are able to indicate changes of order from non-crystalline to crystalline packings. However, not all of them are sensitive enough to indicate different stages of structure transformation under densification. The characteristics based on Delaunay simplices turn out to be the most sensitive for this purpose. For the models considered three principal structure classes are found: packings of densities lower than the known critical value 0.64 showing a non-crystalline behavior; packings with considerable crystalline regions for φ up to 0.66–0.67; rather complete crystals although with numerous defects for φ above 0.67.     

CVM modeling of the square Ising lattice with one next-nearest-neighbor interaction

As an analysis of the development of first-order behavior in two-dimensional Ising lattices, the square lattice with antiferromagnetic nearest-neighbor interactions and a ferromagnetic next-nearest-neighbor interaction in the (11) direction has been modeled. The phase diagram was calculated for a range of interaction parameters and imposed fields; the calculations were performed using the cluster variation method (CVM). Analysis of the calculations suggests that no first-order behavior is developed in this system, so that higher dimensionality or connectivities are required before such behavior is developed.     

Directed Homogeneous Hydrogenation [New Synthetic Methods (65)]

Stereochemical control is a major concern in the application of homogeneous catalysis to organic chemistry. In this context, the directed hydrogenation of olefins employing cationic rhodium or iridium catalysts has considerable potential, for very high selectivity can be attained under mild reaction conditions. The only requirement is a polar functional group in proximity to the double-bond which remains bound to the metal during the catalytic cycle and thereby controls the Stereochemical course of hydrogen delivery through the constraints of chelation. The substituent is most frequently a hydroxy group OH but can also be an ester, amide or carbamate group; other groups remain to be scrutinized. In cyclic compounds, directed hydrogenation can lead to face-selectivity, and the polar substituent may be in the β-, γ-, or δ-position to the double-bond. Acyclic stereoselection ensues with β- or γ-substituents in appropriate compounds, and the configuration of reduced product is predictable on the basis of simple rules. The application of optically active rhodium complexes leads to useful kinetic resolution procedures.     

The Order Parameter of the Chiral Potts Model

An outstanding problem in statistical mechanics is the order parameter of the chiral Potts model. An elegant conjecture for this was made in 1983. It has since been successfully tested against series expansions, but there is as yet no proof of the conjecture. Here we show that if one makes a certain analyticity assumption similar to that used to derive the free energy, then one can indeed verify the conjecture. The method is based on the ‘‘broken rapidity line’’ approach pioneered by Jimbo et al. (J. Phys. A 26:2199--2210 (1993).).     

NeXSPheRIO results on elliptic flow at RHIC and connection with thermalization

Elliptic flow at RHIC is computed event by event with NeXSPheRIO. Reasonable agreement with experimental results on v ₂(η) is obtained. Various effects are studied as well: reconstruction of impact parameter direction, freeze-out temperature, equation of state (with or without crossover), emission mechanism.     

Central elements of the elliptic monodromy matrix algebra at roots of unity

The central elements of the algebra of monodromy matrices associated with the R-matrix are studied. When the crossing parameter w takes a special rational value , where N and n are positive coprime integers, the center is substantially larger than that in the generic case for which the “quantum determinant” provides the center. In the trigonometric limit, the situation corresponds to the quantum group at roots of unity. This is a higher rank generalization of the recent results by Belavin and Jimbo.     

Ternary fission within statistical approach

The ternary system with a light nucleus between two heavy fragments is assumed to appear from the binary configuration near scission. The formation of a third light nucleus in the binary system is considered. The calculated charge distributions in spontaneous ternary fission of ²⁵²Cf and in induced ternary fission of ⁵⁶Ni are compared with the available experimental data. The neutron multiplicity from the fission fragments is described. The fine structures of the TKE-mass distribution are predicted.