Convection cells induced by spontaneous symmetry breaking

Ubiquitous in nature, convection cells are a clear signature of systems out-of-equilibrium. Typically, they are driven by external forces, like gravity (in combination with temperature gradients) or shear. In this article, we show the existence of such cells in possibly the simplest system, one that involves only a temperature gradient. In particular, we consider an Ising lattice gas on a square lattice, in contact with two thermal reservoirs, one at infinite temperature and another at $T$. When this system settles into a non-equilibrium stationary state, many interesting phenomena exist. One of these is the emergence of convection cells, driven by spontaneous symmetry breaking when $T$ is set below the critical temperature.Comment: published version, 2 figures, 5 page

Factorised Steady States in Mass Transport Models on an Arbitrary Graph

We study a general mass transport model on an arbitrary graph consisting of $L$ nodes each carrying a continuous mass. The graph also has a set of directed links between pairs of nodes through which a stochastic portion of mass, chosen from a site-dependent distribution, is transported between the nodes at each time step. The dynamics conserves the total mass and the system eventually reaches a steady state. This general model includes as special cases various previously studied models such as the Zero-range process and the Asymmetric random average process. We derive a general condition on the stochastic mass transport rules, valid for arbitrary graph and for both parallel and random sequential dynamics, that is sufficient to guarantee that the steady state is factorisable. We demonstrate how this condition can be achieved in several examples. We show that our generalized result contains as a special case the recent results derived by Greenblatt and Lebowitz for $d$-dimensional hypercubic lattices with random sequential dynamics.Comment: 17 pages 1 figur

Comment on `Renormalization-Group Calculation of the Dependence on Gravity of the Surface Tension and Bending Rigidity of a Fluid Interface'

It is shown that the interface model introduced in Phys. Rev. Lett. 86, 2369 (2001) violates fundamental symmetry requirements for vanishing gravitational acceleration $g$, so that its results cannot be applied to critical properties of interfaces for $g\to 0$.Comment: A Comment on a recent Letter by J.G. Segovia-L\'opez and V. Romero-Roch\'{\i}n, Phys. Rev. Lett.86, 2369 (2001). Latex file, 1 page (revtex

Roughening transition, surface tension and equilibrium droplet shapes in a two-dimensional Ising system

The exact surface tension for all angles and temperatures is given for the two-dimensional square Ising system with anisotropic nearest-neighbour interactions. Using this in the Wulff construction, droplet shapes are computed and illustrated. Letting temperature approach zero allows explicit study of the roughening transition in this model. Results are compared with those of the solid-on-solid approximation

Driven Diffusive Systems: How Steady States Depend on Dynamics

In contrast to equilibrium systems, non-equilibrium steady states depend explicitly on the underlying dynamics. Using Monte Carlo simulations with Metropolis, Glauber and heat bath rates, we illustrate this expectation for an Ising lattice gas, driven far from equilibrium by an `electric' field. While heat bath and Glauber rates generate essentially identical data for structure factors and two-point correlations, Metropolis rates give noticeably weaker correlations, as if the `effective' temperature were higher in the latter case. We also measure energy histograms and define a simple ratio which is exactly known and closely related to the Boltzmann factor for the equilibrium case. For the driven system, the ratio probes a thermodynamic derivative which is found to be dependent on dynamics

Distributions of absolute central moments for random walk surfaces

We study periodic Brownian paths, wrapped around the surface of a cylinder. One characteristic of such a path is its width square, $w^2$, defined as its variance. Though the average of $w^2$ over all possible paths is well known, its full distribution function was investigated only recently. Generalising $w^2$ to $w^{(N)}$, defined as the $N$-th power of the {\it magnitude} of the deviations of the path from its mean, we show that the distribution functions of these also scale and obtain the asymptotic behaviour for both large and small $w^{(N)}$

Fluctuations and correlations in an individual-based model of biological coevolution

We extend our study of a simple model of biological coevolution to its statistical properties. Staring with a complete description in terms of a master equation, we provide its relation to the deterministic evolution equations used in previous investigations. The stationary states of the mutationless model are generally well approximated by Gaussian distributions, so that the fluctuations and correlations of the populations can be computed analytically. Several specific cases are studied by Monte Carlo simulations, and there is excellent agreement between the data and the theoretical predictions.Comment: 25 pages, 2 figure

Lack of consensus in social systems

We propose an exactly solvable model for the dynamics of voters in a two-party system. The opinion formation process is modeled on a random network of agents. The dynamical nature of interpersonal relations is also reflected in the model, as the connections in the network evolve with the dynamics of the voters. In the infinite time limit, an exact solution predicts the emergence of consensus, for arbitrary initial conditions. However, before consensus is reached, two different metastable states can persist for exponentially long times. One state reflects a perfect balancing of opinions, the other reflects a completely static situation. An estimate of the associated lifetimes suggests that lack of consensus is typical for large systems.Comment: 4 pages, 6 figures, submitted to Phys. Rev. Let