Phase Transitions with Discrete Symmetry Breaking in Antiferromagnetic Heisenberg Models on a Triangular Lattice

We study phase transition behavior of the Heisenberg model on a distorted triangular lattice with competing interactions. The ground-state phase diagram indicates that underlying symmetry can be changed by tuning parameters. We focus on two cases in which a phase transition with discrete symmetry breaking occurs. The first is that the order parameter space is SO(3)$\times C_3$. In this case, a first-order phase transition, with threefold symmetry breaking, occurs. The second has the order parameter space SO(3)$\times Z_2$. In this case, a second-order phase transition occurs with twofold symmetry breaking. To investigate finite-temperature properties of these phase transitions from a microscopic viewpoint, we introduce a method to make the connection between continuous frustrated spin systems and the Potts model with invisible states.Comment: 5 pages, 2 figure

A meshless, integration-free, and boundary-only RBF technique

Based on the radial basis function (RBF), non-singular general solution and dual reciprocity method (DRM), this paper presents an inherently meshless, integration-free, boundary-only RBF collocation techniques for numerical solution of various partial differential equation systems. The basic ideas behind this methodology are very mathematically simple. In this study, the RBFs are employed to approximate the inhomogeneous terms via the DRM, while non-singular general solution leads to a boundary-only RBF formulation for homogenous solution. The present scheme is named as the boundary knot method (BKM) to differentiate it from the other numerical techniques. In particular, due to the use of nonsingular general solutions rather than singular fundamental solutions, the BKM is different from the method of fundamental solution in that the former does no require the artificial boundary and results in the symmetric system equations under certain conditions. The efficiency and utility of this new technique are validated through a number of typical numerical examples. Completeness concern of the BKM due to the only use of non-singular part of complete fundamental solution is also discussed

Arithmetic completely regular codes

In this paper, we explore completely regular codes in the Hamming graphs and related graphs. Experimental evidence suggests that many completely regular codes have the property that the eigenvalues of the code are in arithmetic progression. In order to better understand these "arithmetic completely regular codes", we focus on cartesian products of completely regular codes and products of their corresponding coset graphs in the additive case. Employing earlier results, we are then able to prove a theorem which nearly classifies these codes in the case where the graph admits a completely regular partition into such codes (e.g, the cosets of some additive completely regular code). Connections to the theory of distance-regular graphs are explored and several open questions are posed.Comment: 26 pages, 1 figur

Electrophoresis of a rod macroion under polyelectrolyte salt: Is mobility reversed for DNA?

By molecular dynamics simulation, we study the charge inversion phenomenon of a rod macroion in the presence of polyelectrolyte counterions. We simulate electrophoresis of the macroion under an applied electric field. When both counterions and coions are polyelectrolytes, charge inversion occurs if the line charge density of the counterions is larger than that of the coions. For the macroion of surface charge density equal to that of the DNA, the reversed mobility is realized either with adsorption of the multivalent counterion polyelectrolyte or the combination of electrostatics and other mechanisms including the short-range attraction potential or the mechanical twining of polyelectrolyte around the rod axis.Comment: 8 pages, 5 figures, Applied Statistical Physics of Molecular Engineering (Mexico, 2003). Journal of Physics: Condensed Matters, in press (2004). Journal of Physics: Condensed Matters, in press (2004

Close-packed structures and phase diagram of soft spheres in cylindrical pores

It is shown for a model system consisting of spherical particles confined in cylindrical pores that the first ten close-packed phases are in one-to-one correspondence with the first ten ways of folding a triangular lattice, each being characterized by a roll-up vector like the single-walled carbon nanotube. Phase diagrams in pressure-diameter and temperature-diameter planes are obtained by inherent-structure calculation and molecular dynamics simulation. The phase boundaries dividing two adjacent phases are infinitely sharp in the low-temperature limit but are blurred as temperature is increased. Existence of such phase boundaries explains rich, diameter-sensitive phase behavior unique for cylindrically confined systems

Field-Induced Magnetic Order and Simultaneous Lattice Deformation in TlCuCl3

We report the results of Cu and Cl nuclear magnetic resonance experiments (NMR) and thermal expansion measurements in magnetic fields in the coupled dimer spin system TlCuCl3. We found that the field-induced antiferromagnetic transition as confirmed by the splitting of NMR lines is slightly discontinuous. The abrupt change of the electric field gradient at the Cl sites, as well as the sizable change of the lattice constants, across the phase boundary indicate that the magnetic order is accompanied by simultaneous lattice deformation.Comment: 4 pages, 5 figure