Two harmonically coupled Brownian particles in random media

We study the behaviour of two Brownian particles coupled by an elastic harmonic force in a quenched disordered medium. We found that to first order in disorder strength, the relative motion weakens (with respect to the reference state of a Brownian particle with the double mass) the effect of the quenched forces on the centre of mass motion of the Brownian particles, so that the motion will become less subdiffusive (superdiffusive) for potential (solenoidal) disorder. The mean-square relative distance between the particles behaves in a different way depending of whether the particles are free to move or one particle is anchored in the space. While the effect of nonpotential disorder consists in increasing the mean-square distance in both cases, the potential disorder decreases the mean-square distance, when the particles are free to move, and increases it when one particle is anchored in the space.Comment: 8 pages, 3 figure

Size and doping effects on the coercive field of ferroelectric nanoparticles

A microscopic model for describing ferroelectric nanoparticles is proposed which allows us to calculate the polarization as a function of an external electric field, the temperature, the defect concentration and the particle size. The interaction of the constituents of the material, arranged in layers, depends on both the coupling strength at the surface and that of defect shells in addition to the bulk values. The analysis is based on an Ising model in a transverse field, modified in such a manner to study the influence of size and doping effects on the hysteresis loop of the nanoparticles. Using a Green function technique in real space we find the coercive field, the remanent polarization and the critical temperature which differ significantly from the bulk behavior. Depending on the varying coupling strength due to the kind of doping ions and the surface configuration, the coercive field and the remanent polarization can either increase or decrease in comparison to the bulk behavior. The theoretical results are compared with a variety of different experimental data.Comment: 16 pages, 7 figure

Competing Glauber and Kawasaki Dynamics

Using a quantum formulation of the master equation we study a kinetic Ising model with competing stochastic processes: the Glauber dynamics with probability $p$ and the Kawasaki dynamics with probability $1 - p$. Introducing explicitely the coupling to a heat bath and the mutual static interaction of the spins the model can be traced back exactly to a Ginzburg Landau functional when the interaction is of long range order. The dependence of the correlation length on the temperature and on the probability $p$ is calculated. In case that the spins are subject to flip processes the correlation length disappears for each finite temperature. In the exchange dominated case the system is strongly correlated for each temperature.Comment: 9 pages, Revte

Fluctuation effects in the theory of microphase separation of diblock copolymers in the presence of an electric field

We generalize the Fredrickson-Helfand theory of the microphase separation in symmetric diblock copolymer melts by taking into account the influence of a time-independent homogeneous electric field on the composition fluctuations within the self-consistent Hartree approximation. We predict that electric fields suppress composition fluctuations, and consequently weaken the first-order transition. In the presence of an electric field the critical temperature of the order-disorder transition is shifted towards its mean-field value. The collective structure factor in the disordered phase becomes anisotropic in the presence of the electric field. Fluctuational modulations of the order parameter along the field direction are strongest suppressed. The latter is in accordance with the parallel orientation of the lamellae in the ordered state.Comment: 16 page

Computer simulations of two-dimensional melting with dipole-dipole interactions

We perform molecular dynamics and Monte Carlo simulations of two-dimensional melting with dipole-dipole interactions. Both static and dynamic behaviors are examined. In the isotropic liquid phase, the bond orientational correlation length 6 and susceptibility 6 are measured, and the data are fitted to the theoretical ansatz. An algebraic decay is detected for both spatial and temporal bond orientational correlation functions in an intermediate temperature regime, and it provides an explicit evidence for the existence of the hexatic phase. From the finite-size scaling analysis of the global bond orientational order parameter, the disclination unbinding temperature Ti is estimated. In addition, from dynamic Monte Carlo simulations of the positional order parameter, we extract the critical exponents at the dislocation unbinding temperature Tm. All the results are in agreement with those from experiments and support the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory.Comment: 23 pages, 12figure

Phase Ordering Dynamics of ϕ4\phi^4 Theory with Hamiltonian Equations of Motion

Phase ordering dynamics of the (2+1)- and (3+1)-dimensional $\phi^4$ theory with Hamiltonian equations of motion is investigated numerically. Dynamic scaling is confirmed. The dynamic exponent $z$ is different from that of the Ising model with dynamics of model A, while the exponent $\lambda$ is the same.Comment: to appear in Int. J. Mod. Phys.