End to end distance on contour loops of random gaussian surfaces

A self consistent field theory that describes a part of a contour loop of a random Gaussian surface as a trajectory interacting with itself is constructed. The exponent \nu characterizing the end to end distance is obtained by a Flory argument. The result is compared with different previuos derivations and is found to agree with that of Kondev and Henley over most of the range of the roughening exponent of the random surface.Comment: 7 page

Phase dynamics of a multimode Bose condensate controlled by decay

The relative phase between two uncoupled BE condensates tends to attain a specific value when the phase is measured. This can be done by observing their decay products in interference. We discuss exactly solvable models for this process in cases where competing observation channels drive the phases to different sets of values. We treat the case of two modes which both emit into the input ports of two beam splitters, and of a linear or circular chain of modes. In these latter cases, the transitivity of relative phase becomes an issue

A constrained Potts antiferromagnet model with an interface representation

We define a four-state Potts model ensemble on the square lattice, with the constraints that neighboring spins must have different values, and that no plaquette may contain all four states. The spin configurations may be mapped into those of a 2-dimensional interface in a 2+5 dimensional space. If this interface is in a Gaussian rough phase (as is the case for most other models with such a mapping), then the spin correlations are critical and their exponents can be related to the stiffness governing the interface fluctuations. Results of our Monte Carlo simulations show height fluctuations with an anomalous dependence on wavevector, intermediate between the behaviors expected in a rough phase and in a smooth phase; we argue that the smooth phase (which would imply long-range spin order) is the best interpretation.Comment: 61 pages, LaTeX. Submitted to J. Phys.

Properties of Resonating-Valence-Bond Spin Liquids and Critical Dimer Models

We use Monte Carlo simulations to study properties of Anderson's resonating-valence-bond (RVB) spin-liquid state on the square lattice (i.e., the equal superposition of all pairing of spins into nearest-neighbor singlet pairs) and compare with the classical dimer model (CDM). The latter system also corresponds to the ground state of the Rokhsar-Kivelson quantum dimer model at its critical point. We find that although spin-spin correlations decay exponentially in the RVB, four-spin valence-bond-solid (VBS) correlations are critical, qualitatively like the well-known dimer-dimer correlations of the CDM, but decaying more slowly (as $1/r^a$ with $a \approx 1.20$, compared with $a=2$ for the CDM). We also compute the distribution of monomer (defect) pair separations, which decay by a larger exponent in the RVB than in the CDM. We further study both models in their different winding number sectors and evaluate the relative weights of different sectors. Like the CDM, all the observed RVB behaviors can be understood in the framework of a mapping to a "height" model characterized by a gradient-squared stiffness constant $K$. Four independent measurements consistently show a value $K_{RVB} \approx 1.6 K_{CDM}$, with the same kinds of numerical evaluations of $K_{CDM}$ give results in agreement with the rigorously known value $K_{CDM}=\pi/16$. The background of a nonzero winding number gradient $W/L$ introduces spatial anisotropies and an increase in the effective K, both of which can be understood as a consequence of anharmonic terms in the height-model free energy, which are of relevance to the recently proposed scenario of "Cantor deconfinement" in extended quantum dimer models. We also study ensembles in which fourth-neighbor (bipartite) bonds are allowed, at a density controlled by a tunable fugacity, resulting (as expected) in a smooth reduction of K.Comment: 26 pages, 21 figures. v3: final versio

Stochastic resonance in periodic potentials: realization in a dissipative optical lattice

We have observed the phenomenon of stochastic resonance on the Brillouin propagation modes of a dissipative optical lattice. Such a mode has been excited by applying a moving potential modulation with phase velocity equal to the velocity of the mode. Its amplitude has been characterized by the center-of-mass (CM) velocity of the atomic cloud. At Brillouin resonance, we studied the CM-velocity as a function of the optical pumping rate at a given depth of the potential wells. We have observed a resonant dependence of the CM velocity on the optical pumping rate, corresponding to the noise strength. This corresponds to the experimental observation of stochastic resonance in a periodic potential in the low-damping regime

Logarithmic corrections in the aging of the fully-frustrated Ising model

We study the dynamics of the critical two-dimensional fully-frustrated Ising model by means of Monte Carlo simulations. The dynamical exponent is estimated at equilibrium and is shown to be compatible with the value $z_c=2$. In a second step, the system is prepared in the paramagnetic phase and then quenched at its critical temperature $T_c=0$. Numerical evidences for the existence of logarithmic corrections in the aging regime are presented. These corrections may be related to the topological defects observed in other fully-frustrated models. The autocorrelation exponent is estimated to be $\lambda=d$ as for the Ising chain quenched at $T_c=0$.Comment: 12 pages, 9 figure

Exact Solution of an Octagonal Random Tiling Model

We consider the two-dimensional random tiling model introduced by Cockayne, i.e. the ensemble of all possible coverings of the plane without gaps or overlaps with squares and various hexagons. At the appropriate relative densities the correlations have eight-fold rotational symmetry. We reformulate the model in terms of a random tiling ensemble with identical rectangles and isosceles triangles. The partition function of this model can be calculated by diagonalizing a transfer matrix using the Bethe Ansatz (BA). The BA equations can be solved providing {\em exact} values of the entropy and elastic constants.Comment: 4 pages,3 Postscript figures, uses revte

An exact universal amplitude ratio for percolation

The universal amplitude ratio $\tilde{R}_{\xi}$ for percolation in two dimensions is determined exactly using results for the dilute A model in regime 1, by way of a relationship with the q-state Potts model for q<4.Comment: 5 pages, LaTeX, submitted to J. Phys. A. One paragraph rewritten to correct error

Transverse rotation of the momentary field distribution and the orbital angular momentum of a light beam

The transverse beam pattern, usually observed in experiment, is a result of averaging the optical-frequency oscillations of the electromagnetic field distributed over the beam cross section. An analytical criterion is derived that these oscillations are coupled with a sort of rotation around the beam axis. This criterion appears to be in direct relation with the usual definition of the beam orbital angular momentum.Comment: 9 pages, 1 figure with animatio

On FPL configurations with four sets of nested arches

The problem of counting the number of Fully Packed Loop (FPL) configurations with four sets of a,b,c,d nested arches is addressed. It is shown that it may be expressed as the problem of enumeration of tilings of a domain of the triangular lattice with a conic singularity. After reexpression in terms of non-intersecting lines, the Lindstr\"om-Gessel-Viennot theorem leads to a formula as a sum of determinants. This is made quite explicit when min(a,b,c,d)=1 or 2. We also find a compact determinant formula which generates the numbers of configurations with b=d.Comment: 22 pages, TeX, 16 figures; a new formula for a generating function adde