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Serge Galam

Publications and source records attributed to Serge Galam.

At least 91 records · Page 5Linked to original sources
arXiv2000

From GM Law to A Powerful Mean Field Scheme

A new and powerful mean field scheme is presented. It maps to a one-dimensional finite closed chain in an external field. The chain size accounts for lattice topologies. Moreover lattice connectivity is rescaled according to the GM law recently obtained in percolation theory. The associated self-consistent mean-field equation of state yields critical temperatures which are within a few percent of exact estimates. Results are obtained for a large variety of lattices and dimensions. The Ising lower critical dimension for the onset of phase transitions is $d_l=1+\frac{2}{q}$. For the Ising hypercube it becomes the Golden number $d_l=\frac{1+\sqrt 5}{2}$. The scheme recovers the exact result of no long range order for non-zero temperature Ising triangular antiferromagnets.

cond-mat.dis-nn↗
arXiv2000

Application of Statistical Physics to Politics

The concept and technics of real space renormalization group are applied to study majority rule voting in hierarchical structures. It is found that democratic voting can lead to totalitarianism by keeping in power a small minority. Conditions of this paradox are analyzed and singled out. Indeed majority rule produces critical thresholds to absolute power. Values of these thresholds can vary from 50% up to at least 77%. The associated underlying mechanism could provide an explanation for both former apparent eternity of communist leaderships as well as their sudden collapse.

cond-mat.dis-nn↗
arXiv2000

Optimizing Conflicts in the Formation of Strategic Alliances

Coalition setting among a set of actors (countries, firms, individuals) is studied using concepts from the theory of spin glasses. Given the distribution of respective bilateral propensities to either cooperation or conflict, the phenomenon of local aggregation is modeled. In particular the number of coalitions is determined according to a minimum conflict principle. It is found not to be always two. Along these lines, previous studies are revisited and are found not to be consistent with their own principles. The model is then used to describe the fragmentation of former Yugoslavia. Results are compared to the actual situation.

cond-mat.dis-nn↗
arXiv1999

Metamagnets in uniform and random fields

We study a two-sublattice Ising metamagnet with nearest and next-nearest-neighbor interactions, in both uniform and random fields. Using a mean-field approximation, we show that the qualitative features of the phase diagrams are significantly dependent on the distribution of the random fields. In particular, for a Gaussian distribution of random fields, the behavior of the model is qualitatively similar to a dilute Ising metamagnet in a uniform field.

cond-mat.dis-nn↗
arXiv1999

Behind the shirts, is symmetry

The outbreak of spontaneous order in matter results from symmetry breaking. How does a system change its collective organisation ? How does it break its own symmetry ? That are the questions which are answered using a metaphoric world of shirts and colors.

physics.pop-ph↗
arXiv1999

Comment on "A landscape theory of aggregation"

The problem of aggregation processes in alignments is the subject of a paper published in a Statistical Physics Journal (Physica A 230 (1996) 174-188). Two models are presented and discussed in that paper. First the energy landscape model proposed by Axelrod and Bennett (B. J. Pol. S. 23 (1993) 211-233) is analysed. The model is shown not to include most of its claimed results. Then a second model is presented to reformulate correctly the problem within statistical physics and to extend it beyond the initial Axelrod-Bennett analogy.

cond-mat.dis-nn↗
arXiv1999

Logarithmic Relaxations in a Random Field Lattice Gas Subject to Gravity

A simple lattice gas model with random fields and gravity is introduced to describe a system of grains moving in a disordered environment. Off equilibrium relaxations of bulk density and its two time correlation functions are numerically found to show logarithmic time dependences and "aging" effects. Similitudes with dry granular media are stressed. The connections with off equilibrium dynamics in others kinds of "frustrated" lattice models in presence of a directional driving force (gravity) are discussed to single out the appearance of universal features in the relaxation process.

cond-mat.dis-nn↗
arXiv1999

A new conjecture extends the GM law for percolation thresholds to dynamical situations

The universal law for percolation thresholds proposed by Galam and Mauger (GM) is found to apply also to dynamical situations. This law depends solely on two variables, the space dimension d and a coordinance numberq. For regular lattices, q reduces to the usual coordination number while for anisotropic lattices it is an effective coordination number. For dynamical percolation we conjecture that the law is still valid if we use the number q_2 of second nearest neighbors instead of q. This conjecture is checked for the dynamic epidemic model which considers the percolation phenomenon in a mobile disordered system. The agreement is good.

cond-mat.dis-nn↗
arXiv1999

Spontaneous coalition forming: a model from spin glass

In this paper a simple model is proposed to decribe the spontaneous formation of coalitions among a group of actors like countries. The basic ingredients are from the physics of disorder systems. It is the interplay of two different spin glass models with respectively random bond and random site disorders which is instrumental in the present approach. The cold war stabilty period is then given an explanation as well the instabilities produced by the Warsow pact dissolution. European and Chinese stabilities are also discussed.

cond-mat.dis-nn↗
arXiv1999

A geometrical model for Mixed cyanide crystals

A model of diluted random field sustained by quenched volume deformations is shown to reproduce puzzling physical features found in X(CN)_{x}Y_{1-x} mixed cyanide crystals. X is an alkali metal (K, Na or Rb) and Y is a spherical halogen ion (Br, Cl or I). Critical thresholds x_c at which associated first order ferroelastic transitions disappear are calculated exactly. The diluted random field is shown to compete with compressibility in making the transition first order. Transitions are then found to remain first order down to x_c except in the case of bromine dilution where they become continuous. All the results are in excellent agreement with available experimental data.

cond-mat.dis-nn↗
arXiv1998

Topology invariance in Percolation Thresholds

An universal invariant for site and bond percolation thresholds (p_{cs} and p_{cb} respectively) is proposed. The invariant writes {p_{cs}}^{1/a_s}{p_{cb}}^{-1/a_b}=δ/d where a_s, a_b and δare positive constants,and d the space dimension. It is independent of the coordination number, thus exhibiting a topology invariance at any d.The formula is checked against a large class of percolation problems, including percolation in non-Bravais lattices and in aperiodic lattices as well as rigid percolation. The invariant is satisfied within a relative error of \pm 5% for all the twenty lattices of our sample at d=2, d=3, plus all hypercubes up to d=6.

cond-mat.dis-nn↗
arXiv1998

Competing Species Dynamics: Qualitative Advantage versus Geography

A simple cellular automata model for a two-group war over the same territory is presented. It is shown that a qualitative advantage is not enough for a minority to win. A spatial organization as well a definite degree of aggressiveness are instrumental to overcome a less fitted majority. The model applies to a large spectrum of competing groups: smoker-non smoker war, epidemic spreading, opinion formation, competition for industrial standards and species evolution. In the last case, it provides a new explanation for punctuated equilibria.

cond-mat.dis-nn↗
arXiv1997

A Universal Formula for Percolation Thresholds II. Extension to Anisotropic and Aperiodic Lattices

In a recent paper, we have reported a universal power law for both site and bond percolation thresholds in any Bravais lattice with q equivalent nearest neighbors in dimension d. We now extend it to three different classes of lattices which are, respectively, anisotropic lattices whith not equivalent nearest neighbors, non-Bravais lattices with two atom unit cells, and quasicrystals. The investigation is focussed on d=2 and d=3, due to the lack of experimental data at higher dimensions. The extension to these lattices requires the substitution of q by an effective (non integer) value $q_{eff}$ in the universal law. For each out of 17 lattices which constitute our sample, we argue the existence of one $q_{eff}$ which reproduces both the site and the percolation threshold, with a deviation with respect to numerical estimates which does not exceed $\mp 0.01$.

cond-mat.dis-nn↗
arXiv1997

Rational Group Decision Making. A random field Ising model at T=0

A modified version of a finite random field Ising ferromagnetic model in an external magnetic field at zero temperature is presented to describe group decision making. Fields may have a non-zero average. A postulate of minimum inter-individual conflicts is assumed. Interactions then produce a group polarization along one very choice which is however randomly selected. A small external social pressure is shown to have a drastic effect on the polarization. Individual bias related to personal backgrounds, cultural values and past experiences are introduced via quenched local competing fields. They are shown to be instrumental in generating a larger spectrum of collective new choices beyond initial ones. In particular, compromise is found to result from the existence of individual competing bias. Conflict is shown to weaken group polarization. The model yields new psycho-sociological insights about consensus and compromise in groups.

cond-mat.dis-nn↗
arXiv1997

Diluted Random Fields in Mixed Cyanide Crystals

A percolation argument and a dilute compressible random field Ising model are used to present a simple model for mixed cyanide crystals. The model reproduces quantitatively several features of the phase diagrams altough some crude approximations are made. In particular critical thresholds x_c at which ferroelastic first order transitions disappear, are calculated. Moreover, transitions are found to remain first order down to x_c for all mixtures except for bromine, for which the transition becomes continuous. All the results are in full agreement with experimental data.

cond-mat.dis-nn↗
arXiv1996

A Quasi-exact Formula for Ising critical temperatures on Hypercubic Lattices

We report a quasi-exact power law behavior for Ising critical temperatures on hypercubes. It reads $J/k_BT_c=K_0[(1-1/d)(q-1)]^a$ where $K_0=0.6260356$, $a=0.8633747$, $d$ is the space dimension, $q$ the coordination number ($q=2d$), $J$ the coupling constant, $k_B$ the Boltzman constant and $T_c$ the critical temperature. Absolute errors from available exact estimates ($d=2$ up to $d=7$) are always less than $0.0005$. Extension to other lattices is discussed.

cond-mat↗
arXiv1996

Self-consistency and Symmetry in d-dimensions

Bethe approximation is shown to violate Bravais lattices translational invariance. A new scheme is then presented which goes over the one-site Weiss model yet preserving initial lattice symmetry. A mapping to a one-dimensional finite closed chain in an external field is obtained. Lattice topology determines the chain size. Using recent results in percolation, lattice connectivity between chains is argued to be $(q(d-1)-2)/(d)$ where $q$ is the coordination number and $d$ is the space dimension. A new self-consistent mean-field equation of state is derived. Critical temperatures are thus calculated for a large variety of lattices and dimensions. Results are within a few percent of exact estimates. Moreover onset of phase transitions is found to occur in the range $(d-1)q> 2$. For the Ising hypercube it yields the Golden number limit $d > (1+\sqrt 5)/(2)$.

cond-mat↗