The third parafermionic chiral algebra with the symmetry Z_{3}

We have constructed the parafermionic chiral algebra with the principal parafermionic fields \Psi,\Psi^{+} having the conformal dimension \Delta_{\Psi}=8/3 and realizing the symmetry Z_{3}.Comment: 6 pages, no figur

Renormalization group flows for the second ZNZ_{N} parafermionic field theory for N odd

Using the renormalization group approach, the Coulomb gas and the coset techniques, the effect of slightly relevant perturbations is studied for the second parafermionic field theory with the symmetry $Z_{N}$, for N odd. New fixed points are found and classified

Higher moments of spin-spin correlation functions for the ferromagnetic random bond Potts model

Using CFT techniques, we compute the disorder-averaged p-th power of the spin-spin correlation function for the ferromagnetic random bonds Potts model. We thus generalize the calculation of Dotsenko, Dotsenko and Picco, where the case p=2 was considered. Perturbative calculations are made up to the second order in epsilon (epsilon being proportional to the central charge deviation of the pure model from the Ising model value). The explicit dependence of the correlation function on $p$ gives an upper bound for the validity of the expansion, which seems to be valid, in the three-states case, only if p-alpha in final formula

Parafermionic theory with the symmetry Z_N, for N even

Following our previous papers (hep-th/0212158 and hep-th/0303126) we complete the construction of the parafermionic theory with the symmetry Z_N based on the second solution of Fateev-Zamolodchikov for the corresponding parafermionic chiral algebra. In the present paper we construct the Z_N parafermionic theory for N even. Primary operators are classified according to their transformation properties under the dihedral group (Z_N x Z_2, where Z_2 stands for the Z_N charge conjugation), as two singlets, doublet 1,2,...,N/2-1, and a disorder operator. In an assumed Coulomb gas scenario, the corresponding vertex operators are accommodated by the Kac table based on the weight lattice of the Lie algebra D_{N/2}. The unitary theories are representations of the coset SO_n(N) x SO_2(N) / SO_{n+2}(N), with n=1,2,.... We suggest that physically they realise the series of multicritical points in statistical systems having a Z_N symmetry

"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

Nonstationary westward translation of nonlinear frontal warm-core eddies

For the first time, an analytical theory and a very high-resolution, frontal numerical model, both based on the unsteady, nonlinear, reduced-gravity shallow water equations on a beta plane, have been used to investigate aspects of the migration of homogeneous surface, frontal warm-core eddies on a beta plane. Under the assumption that, initially, such vortices are surface circular anticyclones of paraboloidal shape and having both radial and azimuthal velocities that are linearly dependent on the radial coordinate (i.e., circular pulsons of the first order), approximate analytical expressions are found that describe the nonstationary trajectories of their centers of mass for an initial stage as well as for a mature stage of their westward migration. In particular, near-inertial oscillations are evident in the initial migration stage, whose amplitude linearly increases with time, as a result of the unbalanced vortex initial state on a beta plane. Such an initial amplification of the vortex oscillations is actually found in the first stage of the evolution of warm-core frontal eddies simulated numerically by means of a frontal numerical model initialized using the shape and velocity fields of circular pulsons of the first order. In the numerical simulations, this stage is followed by an adjusted, complex nonstationary state characterized by a noticeable asymmetry in the meridional component of the vortex's horizontal pressure gradient, which develops to compensate for the variations of the Coriolis parameter with latitude. Accordingly, the location of the simulated vortex's maximum depth is always found poleward of the location of the simulated vortex's center of mass. Moreover, during the adjusted stage, near-inertial oscillations emerge that largely deviate from the exactly inertial ones characterizing analytical circular pulsons: a superinertial and a subinertial oscillation in fact appear, and their frequency difference is found to be an increasing function of latitude. A comparison between vortex westward drifts simulated numerically at different latitudes for different vortex radii and pulsation strengths and the corresponding drifts obtained using existing formulas shows that, initially, the simulated vortex drifts correspond to the fastest predicted ones in many realistic cases. As time elapses, however, the development of a beta-adjusted vortex structure, together with the effects of numerical dissipation, tend to slow down the simulated vortex drift

Universality of coupled Potts models

We study systems of M Potts models coupled by their local energy density. Each model is taken to have a distinct number of states, and the permutational symmetry S_M present in the case of identical coupled models is thus broken initially. The duality transformations within the space of 2^M-1 multi-energy couplings are shown to have a particularly simple form. The selfdual manifold has dimension D_M = 2^{M-1}-1. Specialising to the case M=3, we identify a unique non-trivial critical point in the three-dimensional selfdual space. We compare its critical exponents as computed from the perturbative renormalisation group with numerical transfer matrix results. Our main objective is to provide evidence that at the critical point of three different coupled models the symmetry S_3 is restored.Comment: 29 pages, 3 figure

Nonlinear transverse oscillations of a geostrophic front

A planar problem of nonlinear transverse oscillations of the surface (warm) front of a finite width is considered within the framework of a reduced-gravity model of the ocean. The source of oscillations is the departure of the front from its geostrophic equilibrium. When the current velocity is linear in the horizontal coordinate and the front's depth is quadratic in this coordinate, the problem is reduced to a system of four ordinary differential equations in time. As a result, the solution is obtained in a weakly nonlinear approximation and strongly nonlinear oscillations of the front are studied by numerically solving this system of equations by the Runge-Kutta method. The front's oscillations are always superinertial. Nonlinearity can lead to a decrease or increase in the oscillation frequency in comparison with the linear case. The oscillations are most intense when the current velocity is disturbed in the direction of the front's axis. A weakly nonlinear solution of the second order describes the oscillations very accurately even for initial velocity disturbances reaching 50% of its geostrophic value. An increase in the background-current shear leads to the damping of oscillations of the front's boundary. The amplitude of oscillations of the current velocity increases as the intensity of disturbances increases, and it is relatively small if background-current shears are small or large