"Soft power" as an instrument for external political influence of the South Korea

An alternative approach to exercising political influence through "soft power" by South Korea is viewed. Instruments used by Korean diplomacy in its pursuit of its goals are described

Replica Symmetry Breaking and the Renormalization Group Theory of the Weakly Disordered Ferromagnet

We study the critical properties of the weakly disordered $p$-component ferromagnet in terms of the renormalization group (RG) theory generalized to take into account the replica symmetry breaking (RSB) effects coming from the multiple local minima solutions of the mean-field equations. It is shown that for $p < 4$ the traditional RG flows at dimensions $D=4-\epsilon$, which are usually considered as describing the disorder-induced universal critical behavior, are unstable with respect to the RSB potentials as found in spin glasses. It is demonstrated that for a general type of the Parisi RSB structures there exists no stable fixed points, and the RG flows lead to the {\it strong coupling regime} at the finite scale $R_{*} \sim \exp(1/u)$, where $u$ is the small parameter describing the disorder. The physical concequences of the obtained RG solutions are discussed. In particular, we argue, that discovered RSB strong coupling phenomena indicate on the onset of a new spin glass type critical behaviour in the temperature interval $\tau < \tau_{*} \sim \exp(-1/u)$ near $T_{c}$. Possible relevance of the considered RSB effects for the Griffith phase is also discussed.Comment: 32 pages, Late

Entanglement entropy of highly degenerate states and fractal dimensions

We consider the bipartite entanglement entropy of ground states of extended quantum systems with a large degeneracy. Often, as when there is a spontaneously broken global Lie group symmetry, basis elements of the lowest-energy space form a natural geometrical structure. For instance, the spins of a spin-1/2 representation, pointing in various directions, form a sphere. We show that for subsystems with a large number m of local degrees of freedom, the entanglement entropy diverges as (d/2) log m, where d is the fractal dimension of the subset of basis elements with nonzero coefficients. We interpret this result by seeing d as the (not necessarily integer) number of zero-energy Goldstone bosons describing the ground state. We suggest that this result holds quite generally for largely degenerate ground states, with potential applications to spin glasses and quenched disorder.Comment: 5 pages. v2: Small changes, published versio

Critical region of the random bond Ising model

We describe results of the cluster algorithm Special Purpose Processor simulations of the 2D Ising model with impurity bonds. Use of large lattices, with the number of spins up to $10^6$, permitted to define critical region of temperatures, where both finite size corrections and corrections to scaling are small. High accuracy data unambiguously show increase of magnetization and magnetic susceptibility effective exponents $\beta$ and $\gamma$, caused by impurities. The $M$ and $\chi$ singularities became more sharp, while the specific heat singularity is smoothed. The specific heat is found to be in a good agreement with Dotsenko-Dotsenko theoretical predictions in the whole critical range of temperatures.Comment: 11 pages, 16 figures (674 KB) by request to authors: [email protected] or [email protected], LITP-94/CP-0

Cooperative behavior of qutrits with dipole-dipole interactions

We have identified a class of many body problems with analytic solution beyond the mean-field approximation. This is the case where each body can be considered as an element of an assembly of interacting particles that are translationally frozen multi-level quantum systems and that do not change significantly their initial quantum states during the evolution. In contrast, the entangled collective state of the assembly experiences an appreciable change. We apply this approach to interacting three-level systems.Comment: 5 pages, 3 figures. Minor correction

Current-mediated synchronization of a pair of beating non-identical flagella

The basic phenomenology of experimentally observed synchronization (i.e., a stochastic phase locking) of identical, beating flagella of a biflagellate alga is known to be captured well by a minimal model describing the dynamics of coupled, limit-cycle, noisy oscillators (known as the noisy Kuramoto model). As demonstrated experimentally, the amplitudes of the noise terms therein, which stem from fluctuations of the rotary motors, depend on the flagella length. Here we address the conceptually important question which kind of synchrony occurs if the two flagella have different lengths such that the noises acting on each of them have different amplitudes. On the basis of a minimal model, too, we show that a different kind of synchrony emerges, and here it is mediated by a current carrying, steady-state; it manifests itself via correlated "drifts" of phases. We quantify such a synchronization mechanism in terms of appropriate order parameters $Q$ and $Q_{\cal S}$ - for an ensemble of trajectories and for a single realization of noises of duration ${\cal S}$, respectively. Via numerical simulations we show that both approaches become identical for long observation times ${\cal S}$. This reveals an ergodic behavior and implies that a single-realization order parameter $Q_{\cal S}$ is suitable for experimental analysis for which ensemble averaging is not always possible.Comment: 10 pages, 2 figure

Effect of Random Impurities on Fluctuation-Driven First Order Transitions

We analyse the effect of quenched uncorrelated randomness coupling to the local energy density of a model consisting of N coupled two-dimensional Ising models. For N>2 the pure model exhibits a fluctuation-driven first order transition, characterised by runaway renormalisation group behaviour. We show that the addition of weak randomness acts to stabilise these flows, in such a way that the trajectories ultimately flow back towards the pure decoupled Ising fixed point, with the usual critical exponents alpha=0, nu=1, apart from logarithmic corrections. We also show by examples that, in higher dimensions, such transitions may either become continuous or remain first order in the presence of randomness.Comment: 13 pp., LaTe

The One-dimensional KPZ Equation and the Airy Process

Our previous work on the one-dimensional KPZ equation with sharp wedge initial data is extended to the case of the joint height statistics at n spatial points for some common fixed time. Assuming a particular factorization, we compute an n-point generating function and write it in terms of a Fredholm determinant. For long times the generating function converges to a limit, which is established to be equivalent to the standard expression of the n-point distribution of the Airy process.Comment: 15 page