International Journal of Modern Physics C

We introduce a new two-dimensional model with diagonal four spin exchange and an exactly known ground-state. Using variational ansätze and exact diagonalisation we calculate upper and lower bounds for the critical coupling of the model. Both for this model and for the Shastry–Sutherland model we study periodic systems up to system size 6×6.

Transfer matrix calculations of the critical two-point correlation function in 2D Ising model on a finite-size lattice with periodic boundaries along 〈11〉 direction are extended to L = 21. A refined analysis of the correlation function in 〈10〉 crystallographic direction at the distance r = L indicates the existence of a nontrivial finite-size correction of a very small amplitude with correction-to-scaling exponent ω < 2 in agreement with our foregoing study for L ≤ 20. Here we provide an additional evidence and show that amplitude a of the multiplicative correction term 1 + aL^-ω is about -3.5·10^-8 if ω = 1/4 (the expected value). We calculate also the susceptibility for L ≤ 18 in order to compare our numerical estimates for the constant background contribution with the known very precise value and to look for possible nontrivial corrections to scaling. The numerical analysis reveals a perfect agreement for the background term, as well as shows that the nontrivial correction term, detected by our analysis in the correlation function, likely cancels in the susceptibility.

The Heisenberg ferromagnet (uniaxially anisotropic along z-direction), in the presence of time dependent (but uniform over space) magnetic field, is studied by Monte Carlo simulation. The time dependent magnetic field was taken as elliptically polarised in such a way that the resulting field vector rotates in the XZ-plane. In the limit of low anisotropy, the dynamical responses of the system are studied as functions of temperature and the amplitudes of the magnetic field. As the temperature decreases, it was found that the system undergoes multiple dynamical phase transitions. In this limit, the multiple transitions were studied in details and the phase diagram for this observed multicritical behavior was drawn in field amplitude and temperature plane. The natures (continuous/discontinuous) of the transitions are determined by the temperature variations of fourth-order Binder cumulant ratio and the distributions of order parameters near the transition points. The transitions are supported by finite size study. The temperature variations of the variances of dynamic order parameter components (for different system sizes) indicate the existence of diverging length scale near the dynamic transition points. The frequency dependences of the transition temperatures of the multiple dynamic transition are also studied briefly.

A novel thermal lattice Boltzmann (LB) model is proposed to obtain the viscous heat term expediently. Unlike the existing thermal LB models, this model is entirely based on the framework of the LB method and directly derived from the macro temperature equation. Moreover, the computation cost decreases because the computation of complicated material derivative term has been avoided successfully. To testify the simulation capability of this model, the thermal Couette flow is simulated and the results indicate agreement with the analytical solutions.

In order to investigate the dependence on lattice size of several observables in percolation, the Hoshen–Kopelman algorithm was modified so that growing lattices could be simulated. By this way, when simulating a lattice of size L, lattices of smaller sizes can be simulated in the same run for free, saving computing time.

Here, site percolation in three dimensions was studied. Lattices of up to L = 5000, with many L-steps in between, have been simulated, for occupation probabilities of p = 0.25, p = 0.3, p = p_c = 0.311608, and p = 0.35.

The numerical solutions of the unsteady transient-convective diffusion problems are investigated by using multiquadric (MQ) and thin-plate spline (TPS) radial basis functions (RBFs) based on mesh-free collocation methods with global basis functions. The results of radial basis functions are compared with the mesh-dependent boundary element and finite difference methods as well as the analytical solution for high Péclet numbers. It is reported that for low Péclet numbers, MQ-RBF provides excellent agreement, while for high Péclet numbers, TPS-RBF is better than MQ-RBF.

Brief information about nanoparticles and size dependency of their properties is given. Structural properties of copper nanoparticles, Cu_n (n = 50, 100, 150) have been investigated by a modified version of diffusion Monte Carlo method, using an empirical pair potential developed and parameterized for copper. Radial distribution of atoms and the coordination numbers are investigated by the optimum geometries obtained. It has been found that stable structures of copper nanoparticles considered have compact spherical shapes.

The structural, vibrational, electronic and QSAR properties of the dipropyl sulfide (DPS) molecule in gas phase have been investigated theoretically by performing semi-empirical molecular orbital (AM1 and PM3), ab initio (RHF) and density functional theory calculations. The geometry of the molecule has been optimized, infrared spectrum (vibrational modes and intensities) and the electronic properties of the molecule have been calculated in its ground state. It has been found that DPS molecule kinetically may not be stable however it is thermodynamically stable.

A two-dimensional finite difference Lattice Boltzmann model for liquid-vapour systems is introduced. Phase separation is achieved using the dimensionless van der Waals equation of state. A force term is added to account for the surface tension. Flux limiters and TVD schemes are used to improve the accuracy of this model.

We consider a protocol to perform the optimal quantum state discrimination of N linearly independent non-orthogonal pure quantum states and present a computational code. Through the extension of the original Hilbert space, it is possible to perform an unitary operation yielding a final configuration, which gives the best discrimination without ambiguity by means of von Neumann measurements. Our goal is to introduce a detailed general mathematical procedure to realize this task by means of semidefinite programming and norm minimization. The former is used to fix which is the best detection probability amplitude for each state of the ensemble. The latter determines the matrix which leads the states to the final configuration. In a final step, we decompose the unitary transformation in a sequence of two-level rotation matrices.

We discuss the three-dimensional Apollonian network introduced by Andrade et al.¹ for the two-dimensional case. These networks are simultaneously scale-free, small world, Euclidean, space-filling and matching graphs and have a wide range of applications going from the description of force chains in polydisperse granular packings to the geometry of fully fragmented porous media. Some of the properties of these networks, namely, the connectivity exponent, the clustering coefficient, the shortest path, and vertex betweenness are calculated and found to be particularly rich.

The paper proposes a new model of spin dynamics which can be treated as a model of sociological coupling between individuals. Our approach takes into account two different human features: Gregariousness and individuality. We will show how they affect a psychological distance between individuals and how the distance changes the opinion formation in a social group. Apart from its sociological aplications the model displays the variety of other interesting phenomena like self-organizing ferromagnetic state or a second order phase transition and can be studied from different points of view, e.g., as a model of ferromagnetic fluid, complex evolving network or multiplicative random process.