186 research outputs found
Some recent (and surprising) results on interface and contact line depinning in random media
I give a brief review of results obtained recently at Ecole Normale on the
depinning transition of interfaces and contact lines using a variety of
approaches: non-local Monte Carlo algorithms, dynamical renormalization group
calculations to 2-loop order, and exact solution of an infinite-range model.Comment: 10 pages, 2 figures. Talk given at "Horizons in complex Systems"
(Messina, December 2001), to be published in Physica
Phase diagram of a Schelling segregation model
The collective behavior in a variant of Schelling's segregation model is
characterized with methods borrowed from statistical physics, in a context
where their relevance was not conspicuous. A measure of segregation based on
cluster geometry is defined and several quantities analogous to those used to
describe physical lattice models at equilibrium are introduced. This physical
approach allows to distinguish quantitatively several regimes and to
characterize the transitions between them, leading to the building of a phase
diagram. Some of the transitions evoke empirical sudden ethnic turnovers. We
also establish links with 'spin-1' models in physics. Our approach provides
generic tools to analyze the dynamics of other socio-economic systems
New technique for replica symmetry breaking with application to the SK-model at and near T=0
We describe a novel method which allows the treatment of high orders of
replica-symmetry-breaking (RSB) at low temperatures as well as at T=0 directly,
without a need for approximations or scaling assumptions. It yields the low
temperature order function q(a,T) in the full range and is
complete in the sense that all observables can be calculated from it. The
behavior of some observables and the finite RSB theory itself is analyzed as
one approaches continuous RSB. The validity and applicability of the
traditional continuous formulation is then scrutinized and a new continuous RSB
formulation is proposed
Monopoly Market with Externality: an Analysis with Statistical Physics and ACE
In this paper, we explore the effects of localised externalities introduced through interaction structures upon the properties of the simplest market model: the discrete choice model with a single homogeneous product and a single seller (the monopoly case). The resulting market is viewed as a complex interactive system with a communication network. Our main goal is to understand how generic properties of complex adaptive systems can enlighten our understanding of the market mechanisms when individual decisions are inter-related. To do so we make use of an ACE (Agent based Computational Economics) approach, and we discuss analogies between simulated market mechanisms and classical collective phenomena studied in Statistical Physics. More precisely, we consider discrete choice models where the agents are subject to local positive externality. We compare two extreme special cases, the McFadden (McF) and the Thurstone (TP) models. In the McF model the individuals' willingness to pay are heterogeneous, but remain fixed. In the TP model, all the agents have the same homogeneous part of willingness to pay plus an additive random (logistic) idiosyncratic characteristic. We show that these models are formally equivalent to models studied in the Physics literature, the McF case corresponding to a `Random Field Ising model' (RFIM) at zero temperature, and the TP case to an Ising model at finite temperature in a uniform (non random) external field. From the physicist's point of view, the McF and the TP models are thus quite different: they belong to the classes of, respectively,`quenched' and `annealed' disorder, which are known to lead to very different aggregate behaviour. This paper explores some consequences for market behaviour. Considering the optimisation of profit by the monopolist, we exhibit a new `first order phase transition': if the social influence is strong enough, there is a regime where, if the mean willingness to pay increases, or if the production costs decreases, the optimal solution for the monopolist jumps from a solution with a high price and a small number of buyers, to a solution with a low price and a large number of buyers.Agent-Based Computational Economics, discret choices, consumers externality, complex adaptive system, phase transition, avalanches, interactions, hysteresis.
Schelling segregation in an open city: a kinetically constrained Blume-Emery-Griffiths spin-1 system
In the 70's Schelling introduced a multi-agent model to describe the
segregation dynamics that may occur with individuals having only weak
preferences for 'similar' neighbors. Recently variants of this model have been
discussed, in particular, with emphasis on the links with statistical physics
models. Whereas these models consider a fixed number of agents moving on a
lattice, here we present a version allowing for exchanges with an external
reservoir of agents. The density of agents is controlled by a parameter which
can be viewed as measuring the attractiveness of the city-lattice. This model
is directly related to the zero-temperature dynamics of the
Blume-Emery-Griffiths (BEG) spin-1 model, with kinetic constraints. With a
varying vacancy density, the dynamics with agents making deterministic
decisions leads to a new variety of "phases" whose main features are the
characteristics of the interfaces between clusters of agents of different
types. The domains of existence of each type of interface are obtained
analytically as well as numerically. These interfaces may completely isolate
the agents leading to another type of segregation as compared to what is
observed in the original Schelling model, and we discuss its possible
socio-economic correlates.Comment: 10 pages, 7 figures, final version accepted for publication in PR
The branching structure of diffusion-limited aggregates
I analyze the topological structures generated by diffusion-limited
aggregation (DLA), using the recently developed "branched growth model". The
computed bifurcation number B for DLA in two dimensions is B ~ 4.9, in good
agreement with the numerically obtained result of B ~ 5.2. In high dimensions,
B -> 3.12; the bifurcation ratio is thus a decreasing function of
dimensionality. This analysis also determines the scaling properties of the
ramification matrix, which describes the hierarchy of branches.Comment: 6 pages, 1 figure, Euro-LaTeX styl
Double Criticality of the Sherrington-Kirkpatrick Model at T=0
Numerical results up to 42nd order of replica symmetry breaking (RSB) are
used to predict the singular structure of the SK spin glass at T=0. We confirm
predominant single parameter scaling and derive corrections for the T=0 order
function q(a), related to a Langevin equation with pseudotime 1/a. a=0 and
a=\infty are shown to be two critical points for \infty-RSB, associated with
two discrete spectra of Parisi block size ratios, attached to a continuous
spectrum. Finite-RSB-size scaling, associated exponents, and T=0-energy are
obtained with unprecedented accuracy.Comment: 4 pages, 5 figure
The statistical mechanics of combinatorial optimization problems with site disorder
We study the statistical mechanics of a class of problems whose phase space
is the set of permutations of an ensemble of quenched random positions.
Specific examples analyzed are the finite temperature traveling salesman
problem on several different domains and various problems in one dimension such
as the so called descent problem. We first motivate our method by analyzing
these problems using the annealed approximation, then the limit of a large
number of points we develop a formalism to carry out the quenched calculation.
This formalism does not require the replica method and its predictions are
found to agree with Monte Carlo simulations. In addition our method reproduces
an exact mathematical result for the Maximum traveling salesman problem in two
dimensions and suggests its generalization to higher dimensions. The general
approach may provide an alternative method to study certain systems with
quenched disorder.Comment: 21 pages RevTex, 8 figure
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