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

On chaos in mean field spin glasses

We study the correlations between two equilibrium states of SK spin glasses at different temperatures or magnetic fields. The question, presiously investigated by Kondor and Kondor and V\'egs\"o, is approached here constraining two copies of the same system at different external parameters to have a fixed overlap. We find that imposing an overlap different from the minimal one implies an extensive cost in free energy. This confirms by a different method the Kondor's finding that equilibrium states corresponding to different values of the external parameters are completely uncorrelated. We also consider the Generalized Random Energy Model of Derrida as an example of system with strong correlations among states at different temperatures.Comment: 19 pages, Late

Critical behavior of disordered systems with replica symmetry breaking

A field-theoretic description of the critical behavior of weakly disordered systems with a $p$-component order parameter is given. For systems of an arbitrary dimension in the range from three to four, a renormalization group analysis of the effective replica Hamiltonian of the model with an interaction potential without replica symmetry is given in the two-loop approximation. For the case of the one-step replica symmetry breaking, fixed points of the renormalization group equations are found using the Pade-Borel summing technique. For every value $p$, the threshold dimensions of the system that separate the regions of different types of the critical behavior are found by analyzing those fixed points. Specific features of the critical behavior determined by the replica symmetry breaking are described. The results are compared with those obtained by the $\epsilon$-expansion and the scope of the method applicability is determined.Comment: 18 pages, 2 figure

The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class

We explain the exact solution of the 1+1 dimensional Kardar-Parisi-Zhang equation with sharp wedge initial conditions. Thereby it is confirmed that the continuum model belongs to the KPZ universality class, not only as regards to scaling exponents but also as regards to the full probability distribution of the height in the long time limit.Comment: Proceedings StatPhys 2

On touching random surfaces, two-dimensional quantum gravity and non-critical string theory

A set of physical operators which are responsible for touching interactions in the framework of c<1 unitary conformal matter coupled to 2D quantum gravity is found. As a special case the non-critical bosonic strings are considered. Some analogies with four dimensional quantum gravity are also discussed, e.g. creation-annihilation operators for baby universes, Coleman mechanism for the cosmological constant.Comment: 22 pages, Latex2e, 3 figure

Free boson formulation of boundary states in W_3 minimal models and the critical Potts model

We develop a Coulomb gas formalism for boundary conformal field theory having a $W$ symmetry and illustrate its operation using the three state Potts model. We find that there are free-field representations for six $W$ conserving boundary states, which yield the fixed and mixed physical boundary conditions, and two $W$ violating boundary states which yield the free and new boundary conditions. Other $W$ violating boundary states can be constructed but they decouple from the rest of the theory. Thus we have a complete free-field realization of the known boundary states of the three state Potts model. We then use the formalism to calculate boundary correlation functions in various cases. We find that the conformal blocks arising when the two point function of $\phi_{2,3}$ is calculated in the presence of free and new boundary conditions are indeed the last two solutions of the sixth order differential equation generated by the singular vector.Comment: 25 page

The Wandering Exponent of a One-Dimensional Directed Polymer in a Random Potential with Finite Correlation Radius

We consider a one-dimensional directed polymer in a random potential which is characterized by the Gaussian statistics with the finite size local correlations. It is shown that the well-known Kardar's solution obtained originally for a directed polymer with delta-correlated random potential can be applied for the description of the present system only in the high-temperature limit. For the low temperature limit we have obtained the new solution which is described by the one-step replica symmetry breaking. For the mean square deviation of the directed polymer of the linear size L it provides the usual scaling $L^{2z}$ with the wandering exponent z = 2/3 and the temperature-independent prefactor.Comment: 14 pages, Late

Self-avoiding random surfaces with fluctuating topology

A gas of self-avoiding surfaces with an arbitrary polynomial coupling to the gaussian curvature and an extrinsic curvature term can be realized in a three-dimensional Ising bcc lattice with only three local couplings. Similar three parameter realizations are valid also in other lattices. The relation between the crumpling transition and the roughening is discussed. It turns out that the mean area of these surfaces is proportional to its genus.Comment: 4 pages , uuencoded .ps file with two figures included.( Contribution to Lattice 93, Dallas

Boundary critical behaviour of two-dimensional random Ising models

Using Monte Carlo techniques and a star-triangle transformation, Ising models with random, 'strong' and 'weak', nearest-neighbour ferromagnetic couplings on a square lattice with a (1,1) surface are studied near the phase transition. Both surface and bulk critical properties are investigated. In particular, the critical exponents of the surface magnetization, 'beta_1', of the correlation length, 'nu', and of the critical surface correlations, 'eta_{\parallel}', are analysed.Comment: 16 pages in ioplppt style, 7 ps figures, submitted to J. Phys.

A Non-Perturbative Approach to the Random-Bond Ising Model

We study the N -> 0 limit of the O(N) Gross-Neveu model in the framework of the massless form-factor approach. This model is related to the continuum limit of the Ising model with random bonds via the replica method. We discuss how this method may be useful in calculating correlation functions of physical operators. The identification of non-perturbative fixed points of the O(N) Gross-Neveu model is pursued by its mapping to a WZW model.Comment: 17 pages LaTeX, 1 PostScript figure included using psfig.st