Avoiding Chaos in Wonderland

Wonderland, a compact, integrated economic, demographic and environmental model is investigated using methods developed for studying critical phenomena. Simulation results show the parameter space separates into two phases, one of which contains the property of long term, sustainable development. By employing information contain in the phase diagram, an optimal strategy involving pollution taxes is developed as a means of moving a system initially in a unsustainable region of the phase diagram into a region of sustainability while ensuring minimal regret with respect to long term economic growth.Comment: 22 pages, 9 figures. Submitted to Physica

Hyperscaling in the Domany-Kinzel Cellular Automaton

An apparent violation of hyperscaling at the endpoint of the critical line in the Domany-Kinzel stochastic cellular automaton finds an elementary resolution upon noting that the order parameter is discontinuous at this point. We derive a hyperscaling relation for such transitions and discuss applications to related examples.Comment: 8 pages, latex, no figure

Replica Symmetry Breaking in Attractor Neural Network Models

The phenomenon of replica symmetry breaking is investigated for the retrieval phases of Hopfield-type network models. The basic calculation is done for the generalized version of the standard model introduced by Horner [1] and by Perez-Vicente and Amit [2] which can exhibit low mean levels of neural activity. For a mean activity $\bar a =1/2$ the Hopfield model is recovered. In this case, surprisingly enough, we cannot confirm the well known one step replica symmetry breaking (1RSB) result for the storage capacity which was presented by Crisanti, Amit and Gutfreund [3] (\alpha_c^{\hbox{\mf 1RSB}}\simeq 0.144). Rather, we find that 1RSB- and 2RSB-Ans\"atze yield only slightly increased capacities as compared to the replica symmetric value (\alpha_c^{\hbox{\mf 1RSB}}\simeq 0.138\,186 and \alpha_c^{\hbox{\mf 2RSB}}\simeq 0.138\,187 compared to \alpha_c^{\hbox{\mf RS}}\simeq 0.137\,905), significantly smaller also than the value \alpha_c^{\hbox{\mf sim}} = 0.145\pm 0.009 reported from simulation studies. These values still lie within the recently discovered reentrant phase [4]. We conjecture that in the infinite Parisi-scheme the reentrant behaviour disappears as is the case in the SK-spin-glass model (Parisi--Toulouse-hypothesis). The same qualitative results are obtained in the low activity range.Comment: Latex file, 20 pages, 8 Figures available from the authors upon request, HD-TVP-94-

A vortex description of the first-order phase transition in type-I superconductors

Using both analytical arguments and detailed numerical evidence we show that the first order transition in the type-I 2D Abelian Higgs model can be understood in terms of the statistical mechanics of vortices, which behave in this regime as an ensemble of attractive particles. The well-known instabilities of such ensembles are shown to be connected to the process of phase nucleation. By characterizing the equation of state for the vortex ensemble we show that the temperature for the onset of a clustering instability is in qualitative agreement with the critical temperature. Below this point the vortex ensemble collapses to a single cluster, which is a non-extensive phase, and disappears in the absence of net topological charge. The vortex description provides a detailed mechanism for the first order transition, which applies at arbitrarily weak type-I and is gauge invariant unlike the usual field-theoretic considerations, which rely on asymptotically large gauge coupling.Comment: 4 pages, 6 figures, uses RevTex. Additional references added, some small corrections to the tex

Quasi-stationary distributions for the Domany-Kinzel stochastic cellular automaton

We construct the {\it quasi-stationary} (QS) probability distribution for the Domany-Kinzel stochastic cellular automaton (DKCA), a discrete-time Markov process with an absorbing state. QS distributions are derived at both the one- and two-site levels. We characterize the distribuitions by their mean, and various moment ratios, and analyze the lifetime of the QS state, and the relaxation time to attain this state. Of particular interest are the scaling properties of the QS state along the critical line separating the active and absorbing phases. These exhibit a high degree of similarity to the contact process and the Malthus-Verhulst process (the closest continuous-time analogs of the DKCA), which extends to the scaling form of the QS distribution.Comment: 15 pages, 9 figures, submited to PR

The Ginzburg regime and its effects on topological defect formation

The Ginzburg temperature has historically been proposed as the energy scale of formation of topological defects at a second order symmetry breaking phase transition. More recently alternative proposals which compute the time of formation of defects from the critical dynamics of the system, have been gaining both theoretical and experimental support. We investigate, using a canonical model for string formation, how these two pictures compare. In particular we show that prolonged exposure of a critical field configuration to the Ginzburg regime results in no substantial suppression of the final density of defects formed. These results dismiss the recently proposed role of the Ginzburg regime in explaining the absence of topological defects in 4He pressure quench experiments.Comment: 8 pages, 5 ps figure

A Biased Review of Sociophysics

Various aspects of recent sociophysics research are shortly reviewed: Schelling model as an example for lack of interdisciplinary cooperation, opinion dynamics, combat, and citation statistics as an example for strong interdisciplinarity.Comment: 16 pages for J. Stat. Phys. including 2 figures and numerous reference

Effect of Finite Grain Size on the Simulation of Fluid Flow in Porous Media

Effects caused by the necessarily finite grain size used in simulations of flow porous media are systematically studied in two dimensional hydrodynamic cellular automata with systems of up to 88 million sites. The permeability of the media, K, is found to be a function of the grain size, R, and an extrapolation to physically realistic grain sizes is given

Limitations of a finite mean free path for simulating flows in porous media

When the mean free path, $\lambda$, of fluid particles for Hydrodynamic Cellular Automata is not much smaller than the characteristic length of the system, then hydrodynamic correlations do not have a chance to develop and true hydrodynamic flow will not be obtained. By studying a simple two dimensional system, it is concluded that the finite size corrections to the permeability, $\kappa$, for pore size, R, are of the form: 1 + 7 $\cdot$ ($\lambda / R$). The limitations this result places on the use of such methods for studying flows in porous media is discussed

Calculations of drag coefficients viavia hydrodynamic cellular automata

The drag coefficient, $C_{\rm D}$, of an arbitrary shaped object can be calculated by two-dimensional hydrodynamic cellular automata. Results spanning nearly four orders of magnitude in the Reynolds number ($0.1 < {\rm Re} < 10^{3}$) are presented for a simple, hexagonal object, and good quantitative agreement with previous experiments on cylinders is obtained