International Journal of Modern Physics C

A long-standing issue in a three-dimensional Ising spin glass (3DISG) is to settle the critical exponents. Numerical simulations and a conventional finite-size-scaling analysis have given controversial estimates, in particular, for the value of thermal exponent ν. Here a recently proposed extended scaling scheme is reviewed and illustrated for the canonical two-dimensional Ising ferromagnet. By applying the extended scaling to our extensive Monte Carlo data for 3DISG, consistent estimates of critical parameters are obtained in contrast to previous analyses.

High precision Monte Carlo simulations are used to study domain growth in a compressible two-dimensional spin-exchange Ising model with continuous particle positions and zero total magnetization. For mismatched systems, we measure significant deviations from the theoretically expected late-time domain growth, R(t) = A + Btⁿ with n = 1/3. For a compressible model with no mismatch, we measure only a slight deviation from n = 1/3. Our results indicate that our current understanding of domain growth is incomplete.

Using the mean-field approximation, we study the reorientation transition in a discrete dipolar spin model. We array the d-dimensional spins in the d-1-dimensional hypercubic lattice points, and apply the magnetic anisotropy in the dth direction. Even though the long-range dipolar interaction is truncated to the nearest-neighbor interaction, the model exhibits the reorientation transition. The effects of the exchange interaction on the dipolar system are also studied.

The possible existence of small, pure carbon molecules based on small-world networks is addressed using density functional theory simulations. A ring of atoms with one or more small-world connections between pairs of non-nearest-neighbor sites was chosen for the network topology. The small-world connections are made with and without additional carbon atoms placed along the link. The energy per atom of these small-world carbon systems is compared with benchmark molecules such as the C₂₀ ring, bowl, and cage isomers, the C₆₀ Buckyball, monocyclic pure carbon rings ranging from C₄ to C₆₀, bare linear carbon chains ranging from C₂ to C₃₆, and various graphitic fragments without hydrogens. The results of the energy per atom for some of these small-world clusters provide an indication that such pure carbon molecules are reasonable for real world synthesis.

We study the critical endpoint behavior of an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. We use a two-dimensional Wang–Landau sampling method to determine the density of states for this model. An accurate density of states allowed us to map out the phase diagram accurately and observe a clear divergence of the curvature of the spectator phase boundary and of the derivative of the magnetization coexistence diameter near the critical endpoint, in agreement with previous theoretical predictions.

The q-state clock gauge glass model in two dimensions with q = 6, 8, 10, 12, 14, 16 is studied by the use of the nonequilibrium relaxation analysis of the Kosterlitz–Thouless (KT) transition. The successive transitions of FM-KT-PM phases are investigated along the Nishimori line. For the upper critical temperature, it is found that the transition temperature is almost the same as in the continuous case for all q values. The lower transition temperature is found to be proportional to 1/q². While the present model is not self-dual, we have a remarkable behavior with respect to the duality relation derived for the self-dual Villain-type model.

An exact solution is presented for mixing two or more different types of Random Deposition (RD) nonequilibrium surface growth processes. The depositions may be made in a sequential mode, or in a random mode by first randomly choosing the lattice site for deposition. The results hold in all dimensions d. Simulations are presented in d = 1 for comparison. Furthermore, a mean-field type of approach to mixing RD with other surface growth processes is tested against the exact solution.

We explore the complex dynamical behavior of simple predator-prey models of biological coevolution that account for interspecific and intraspecific competition for resources, as well as adaptive foraging behavior. In long kinetic Monte Carlo simulations of these models we find quite robust 1/f-like noise in species diversity and population sizes, as well as power-law distributions for the lifetimes of individual species and the durations of quiet periods of relative evolutionary stasis. In one model, based on the Holling Type II functional response, adaptive foraging produces a metastable low-diversity phase and a stable high-diversity phase.

In this work we introduce a hybrid ab initio-classical simulation methodology designed to incorporate the chemistry into the description of phenomena that, intrinsically, require very large systems to be properly described. This hybrid approach allows us to conduct large-scale atomistic simulations with a simple classical potential (embedded atom method (EAM), for instance) while simultaneously using a more accurate ab initio approach for critical embedded regions. The coupling is made through shared atomic shells where the two atomistic modeling approaches are relaxed in an iterative, self-consistent manner. The magnitude of the incompatibility forces arising in the shared shell is analyzed, and possible terminations for the embedded region are discussed, as a way to reduce such forces. As a test case, the formation energy of a single vacancy in aluminum at different distances from an edge dislocation is studied. Results obtained using the hybrid approach are compared to those obtained using classical methods alone, and the range of validity for the classical approach is evaluated.

Some recent progress in Monte Carlo simulations of spin glasses will be presented. The problem of slow dynamics at low temperatures is partially alleviated by use of the parallel tempering (replica exchange) method. A useful technique to check for equilibration (applicable only for a Gaussian distribution) will be discussed. It will be argued that a finite size scaling analysis of the scaled correlation length of the system is a good approach with which to investigate phase transitions in spin glasses. This method will be used to study two questions:

(i) whether there is a phase transition in zero field in the Heisenberg spin glass in three dimensions, and

(ii) whether there is phase transition in a magnetic field in an Ising spin glass, also in three dimensions.

We study the low-energy excitation of the quantum spin tube with the triangular lattice structure, using density matrix renormalization group. Taking account of the edge spin effect, we particularly investigate the spin gap behavior and the low-field magnetization curve near the quantum phase transition point in contrast with the usual free boundary condition. We then find that the bulk behavior of the spin tube can be extracted easier for the single spin termination.

The ability to simulate several aspects of two-dimensional quantum mechanics is discussed, in conjunction with an ongoing visualization project, WebTOP, that has been of recognizable importance to physics education since its inception in the late 1990s. In the past, the WebTOP project has been primarily used as a means of visualizing optics and wave phenomena and, now, the development of certain interactive quantum mechanical demonstrations has the potential to strengthen its power as an educational tool for the physics community. The added functionality for propagating wave packets forward in time for a given 2D potential gives rise to the ability to investigate interesting quantum behaviors. Fractional revivals of states in the 2D infinite square well can be clearly seen as well as the time delay of scattered wave packets for certain step potentials. Aspects of squeezed and coherent states of the 2D harmonic oscillator potential can also be explored, among other observable phenomena.

A molecular simulation study of the mesoscale self-assembly of tethered nanoparticles having a cubic geometry is presented. Minimal models of the tethered nanocubes are developed to represent a polyhedral oligomeric silsesquioxane (POSS) molecule with polymeric substituents. The models incorporate some of the essential structural features and interaction specificity of POSS molecules, and facilitate access to the long length and timescales pertinent to the assembly process while foregoing atomistic detail. The types of self-assembled nanostructures formed by the tethered nanocubes in solution are explored via Brownian dynamics simulations using these minimal models. The influence of various parameters, including the conditions of the surrounding medium, the molecular weight and chemical composition of the tether functionalities, and the number of tethers on the nanocube, on the formation of specific structures is demonstrated. The role of cubic nanoparticle geometry on self-assembly is also assessed by comparing the types of structures formed by tethered nanocubes and by their flexible coil triblock copolymer and tethered nanosphere counterparts. Morphological phase diagrams are proposed to describe the behavior of the tethered nanocubes.

A new direct numerical simulation scheme, called "Smoothed Profile (SP) method," is presented. The SP method, as a direct numerical simulation of particulate flow, provides a way to couple continuum fluid dynamics with rigid-body dynamics through smoothed profile of colloidal particle. Our formulation includes extensions to colloids in multicomponent solvents such as charged colloids in electrolyte solutions. This method enables us to compute the time evolutions of colloidal particles, ions, and host fluids simultaneously by solving Newton, advection-diffusion, and Navier–Stokes equations so that the electro-hydrodynamic couplings can be fully taken into account. The electrophoretic mobilities of charged spherical particles are calculated in several situations. The comparisons with approximation theories show quantitative agreements for dilute dispersions without any empirical parameters.

We investigate the elementary excitations and magnetization dynamics of the recently synthesized single-chain magnets, which consist of Mn and Ni ions, and some related systems, using the numerical exact diagonalization of finite-size clusters and the density matrix renormalization group method. It is found that, as the easy-axis anisotropy D increases, a crossover of the lowest-lying elementary excitation should exist between the spin wave and Ising-like excitations. For the realistic trimer single-chain magnet, we estimate several crossover temperatures. In addition we predict that a magnetization plateau at 2/3 of the saturation magnetization would appear in the (s, S) = (1, 2) spin-alternating chain. The phase diagram of the plateau is also presented.

Frustrated metals are investigated by numerical methods. In the absence of fermionic dynamics, the models are equivalent to a frustrated Ising model on a geometrically frustrated lattice, where macroscopic degeneracies are observed in the ground states. By taking into account fermionic hoppings, the models show partial loss of degeneracy, but still remains to be frustrated. Various properties of the system, including charge correlations, are also examined.

We study the distribution of ions and water within a pore in a polarizable membrane, in the presence of a stiff polyelectrolyte threaded through the pore. In this system, which represents a typical situation during the translocation of DNA, the distribution of both the ions and the water molecules is affected by the induced charges on the surface of the polarizable nanopore. Specifically, the concentration of counterions is enhanced near the surface of the pore, due to the attractive interaction with the induced charges. Conversely, the water within the pore is depleted, as a result of the disruption of hydrogen bonds by the induced charges.