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A fair assignment of credit for multi-authored publications is a long-standing issue in scientometrics. In the calculation of the $h$-index, for instance, all co-authors receive equal credit for a given publication, independent of a given author's contribution to the work or of the total number of co-authors. Several attempts have been made to distribute the credit in a more appropriate manner. In a recent paper, Hirsch has suggested a new way of credit assignment that is fundamentally different from the previous ones: All credit for a multi-author paper goes to a single author, the called ``$\alpha$-author'', defined as the person with the highest current $h$-index not the highest $h$-index at the time of the paper's publication) (J. E. Hirsch, Scientometrics 118, 673 (2019)). The collection of papers this author has received credit for as $\alpha$-author is then used to calculate a new index, $h_{\alpha}$, following the same recipe as for the usual $h$ index. The objective of this new assignment is not a fairer distribution of credit, but rather the determination of an altogether different property, the degree of a person's scientific leadership. We show that given the complex time dependence of $h$ for individual scientists, the approach of using the current $h$ value instead of the historic one is problematic, and we argue that it would be feasible to determine the $\alpha$-author at the time of the paper's publication instead. On the other hand, there are other practical considerations that make the calculation of the proposed $h_{\alpha}$ very difficult. As an alternative, we explore other ways of crediting papers to a single author in order to test early career achievement or scientific leadership., Comment: 6 pages, 4 figures

The Trump phenomenon is argued to depart from current populist rise in Europe. According to a model of opinion dynamics from sociophysics the machinery of Trump's amazing success obeys well-defined counter-intuitive rules. Therefore, his success was in principle predictable from the start. The model uses local majority rule arguments and obeys a threshold dynamics. The associated tipping points are found to depend on the leading collective beliefs, cognitive biases and prejudices of the social group which undertakes the public debate. And here comes the sesame of the Trump campaign, which develops along two successive steps. During a first moment, Trump's statement produces a majority of voters against him. But at the same time, according to the model the shocking character of the statement modifies the prejudice balance. In case the prejudice is present even being frozen among voters, the tipping point is lowered at Trump's benefit. Nevertheless, although the tipping point has been lowered by the activation of frozen prejudices it is instrumental to preserve enough support from openly prejudiced people to be above the threshold. Then, as infuriated voters launch intense debate, occurrence of ties will drive progressively hostile people to shift their voting intention without needing to endorse the statement which has infuriated them. The on going debate does drive towards a majority for Trump. The possible Trump victory at November Presidential election is discussed. In particular, the model shows that to eventually win the Presidential election, Trump must not modify his past shocking attitude but to appeal to a different spectrum of frozen prejudices, which are common to both Democrats and Republicans., Comment: 24 pages, 9 figures, to appear in International Journal of Modern Physics B

We are investigating a paradigm of instability in coalition forming among countries, which indeed is intrinsic to any collection of individual groups or other social aggregations. Coalitions among countries are formed by the respective attraction or repulsion caused by the historical bond propensities between the countries, which produced an intricate circuit of bilateral bonds. Contradictory associations into coalitions occur due to the independent evolution of the bonds. Those coalitions tend to be unstable and break down frequently. The model extends some features of the physical theory of Spin Glasses. Within the frame of this model, the instability is viewed as a consequence of decentralized maximization processes searching for the best coalition allocations. In contrast to the existing literature, a rational instability is found to result from forecast rationality of countries. Using a general theoretical framework allowing to analyze the countries' decision making in coalition forming, we feature a system where stability can eventually be achieved as a result of the maximization processes. We provide a formal implementation of the maximization principles and illustrate it in the multi-thread simulation of the coalition forming. The results shed a new light on the prospect of searches for the best coalition allocations in the networks of social, political or economical entities., 24 pages, 12 Figures

The combined effects of collective beliefs and individual inflexibility in the dynamics of a public debate are investigated using the Galam sequential probabilistic model of opinion dynamics. The study is focused on pair interactions for which the bias produced by collective beliefs is the decisive factor to win the debate. The current value of that bias is a fixed external parameter. It is a constant of the problem not given to change. In contrast, inflexibility is an individual property. It results from external ingredients, which are susceptible to be modified during the debate. More precisely, giving some beliefs we determine the required inflexibility to oppose its associated bias in the debate outcome. The results shed a new and counter intuitive light on paradoxical outcomes of sensitive issues, which are discussed in the public. The cases of global warming issue and debate over evolution are discussed.

According to the classic Galam model of opinion dynamics, each agent participates at each update of an opinion interaction. While the scheme gives everyone the same chance to in- fluence others, in reality, social activity and influence vary considerably from one agent to another. To account for such a feature, we introduce a new individual attribute – ‘‘active- ness’’ – which makes some agents more inclined than others at engaging in local discus- sions. To enhance the corresponding effect, opinion updates are shifted from all-out agent interaction cycles to few agent interaction cycles. Using dynamic analysis and simulations the resulting model is found to exhibit a ‘‘Minority Counteroffensive’’ phenomenon, which under some initial conditions makes the minority to win the opinion competition despite a threshold tipping point at fifty percent. The associated probabilistic phenomenon persists in the case ‘‘activeness’’ is held equal for all agents. The effect of ‘‘opinion leaders’’ is also investigated. Indeed, a leader is an inflexible agent, i.e., an agent who does not change opin- ion. The results reveal that two opinion leaders with moderate social influence may have a stronger effect than one opinion leader with a strong social influence. The model may shed a new light to the understanding of opinion formation and public voting.

We generalize Galam's model of opinion spreading by introducing three competing choices. At each update, the population is randomly divided in groups of three agents, whose members adopt the opinion of the local majority. In the case of a tie, the local group adopts opinion A, B or C with probabilities alpha, beta and (1-alpha-beta) respectively. We derive the associated phase diagrams and dynamics by both analytical means and simulations. Polarization is always reached within very short time scales. We point out situations in which an initially very small minority opinion can invade the whole system., To appear in European Physical Journal B. A few errors corrected, some figures redrawn from the first version

The origins of Sociophysics are discussed from a personal testimony. I trace back its history to the late seventies. My twenty years of activities and research to establish and promote the field are reviewed. In particular the conflicting nature of Sociophysics with the physics community is revealed from my own experience. Recent presentations of a supposed natural growth from Social Sciences are criticized., 7 pages, no figure, Proceedings of the XVIII Max Born Symposium on Statistical Physics outside Physics, Ladek, Poland, September 2003

A model for the dynamics of opinion forming in democratic public debate is presented. Using concepts and techniques from the physics of disorder the dynamics of social refusal spreading is studied within a perfect world, where the minority holds neither better arguments nor lobbying backing. The one-person-one-vote rule, together with local majority rules, are used to determine the outcome of local group discussions. In case of a local tie, the group decides on keeping the Status Quo. The geometry of social life shaped by offices, houses, bars, and restaurants is shown to determine the distribution size of these discussion groups. It is found to yield very asymmetric unstable thresholds to the total spreading of one opinion at the benefit of the refusal one. The associated dynamics is rather quick and completed within few days. This democratic paradox of public debate driven majority opinion reversal is discussed in light of some European construction issues. The model may apply to rumor and fear propagation.

We study the effects of contrarians on the dynamics of opinion forming using the 2-state Galam opinion dynamics model. In a single update step, groups of a given size are defined and all agents in each group adopt the state of the local majority. In the absence of contrarians, the dynamics is fast and leads to a total polarization always along the initial majority (for groups of odd sizes). The introduction of contrarians is then shown to give rise to interesting new dynamics properties. First, at low concentration a, a new mixed phase is stabilized with a coexistence of both states. This is an ordered phase with a clear cut majority–minority splitting (non zero order parameter). Second, there is a phase transition into a new disordered phase at a c = 1 6 , 0.23, 0.30… 1 2 for groups of respective sizes 3, 5, 9 and infinite. For a⩾ac the disordered phase has no opinion dominating with both state densities equal (zero order parameter). In this phase agents keep shifting states but no global symmetry breaking, i.e., the appearance of a majority, takes place. Our results may shed a new light on the phenomenon of “hung elections” as occured in the 2000 American presidential elections and that of the 2002 German parliamentary elections.

The September 11 attack on the US has revealed an unprecedented terrorism with worldwide range of destruction. It is argued to result from the first worldwide percolation of passive supporters. They are people sympathetic to the terrorism cause but without being involved with it. They just don't oppose it in case they could. This scheme puts suppression of the percolation as the major strategic issue in the fight against terrorism. Acting on the population is shown to be useless. Instead a new strategic scheme is suggested to increase the terrorism percolation threshold and in turn suppress the percolation. The relevant associated space is identified as a multi-dimensional social space including both the ground earth surface and all various independent flags displayed by the terrorist group. Some hints are given on how to shrink the geographical spreading of terrorism threat. The model apply to a large spectrum of clandestine activities including guerilla warfare as well as tax evasion, corruption, illegal gambling, illegal prostitution and black markets., 17 pages, 7 figures, Proceedings of the International Workshop Randomness And Complexity in honor of Shlomo Havlin's 60th birthday held in January 2003, Eilat, Israel

The recent astonishing wide adhesion of french people to the rumor claiming `No plane did crash on the Pentagon on September the 11", is given a generic explanation in terms of a model of minority opinion spreading. Using a majority rule reaction-diffusion dynamics, a rumor is shown to invade for sure a social group provided it fulfills simultaneously two criteria. First it must initiate with a support beyond some critical threshold which however, turns out to be always very low. Then it has to be consistent with some larger collective social paradigm of the group. Othewise it just dies out. Both conditions were satisfied in the french case with the associated book sold at more than 200 000 copies in just a few days. The rumor was stopped by the firm stand of most newspaper editors stating it is nonsense. Such an incredible social dynamics is shown to result naturally from an open and free public debate among friends and colleagues. Each one searching for the truth sincerely on a free will basis and without individual biases. The polarization process appears also to be very quick in agreement with reality. It is a very strong anti-democratic reversal of opinion although made quite democratically. The model may apply to a large range of rumors.

Coalition forming is investigated among countries, which are coupled with short range interactions, under the influence of externally-set opposing global alliances. The model extends a recent Natural Model of coalition forming inspired from Statistical Physics, where instabilities are a consequence of decentralized maximization of the individual benefits of actors. In contrast to physics where spins can only evaluate the immediate cost/benefit of a flip of orientation, countries have a long horizon of rationality, which associates with the ability to envision a way up to a better configuration even at the cost of passing through intermediate loosing states. The stabilizing effect is produced through polarization by the global alliances of either a particular unique global interest factor or multiple simultaneous ones. This model provides a versatile theoretical tool for the analysis of real cases and design of novel strategies. Such analysis is provided for several real cases including the Eurozone. The results shed a new light on the understanding of the complex phenomena of planned stabilization in the coalition forming.

The dynamics of opinion about the controversy of abnormal death of bees is studied among French speaking journalists using a corpus of 1467 articles published in newspapers during the period 1998–2010. From a systematic textual analysis, each article is tagged to either one of three stances to explain the phenomenon, a uni-factor cause, namely the use of pesticides, a multi-factor cause, or the absence of an understanding. On this basis, evolutions of the respective proportions of each category are obtained over the 13 consecutive years, exhibiting a series of broken lines. Assuming journalists are either flexible or inflexible about their respective views, their associated proportions are extracted from the data applying Galam Unifying Frame (GUF) of opinion dynamics. The variation of inflexibles along each view is thus obtained as a function of years for the 13 years of the corpus. From those distributions the possible pressure applied on journalists from lobbying or other externalities can be inferred. In addition, the results highlight the critical advantage gained by the first whistle-blowers and underline opinion inertia in the debate.

Majority rule voting in a multi-level system is studied using tools from the physics of disorder. We are not dealing with nation-wide general elections but rather with hierarchical organisations made of small committees. While in theory, for a two candidate election, the critical threshold to absolute power is , the usual existence of some local and reasonable bias makes it asymmetric, transforming a democratic system in effect to a dictatorship. The underlying dynamics of this democratic self-elimination is studied using a simulation which visualizes the full process. In addition the effect of non-voting persons (abstention, sickness, apathy) is also studied. It is found to have an additional drastic effect on the asymmetry of the threshold value to power. Some possible applications are mentioned.

The effect of majority rule voting in hierarchical structures is studied using the basic concepts from real space renormalization group. It shows in particular that a huge majority can be self-eliminated while climbing up the hierarchy levels. This majority democratic self-elimination articulates around the existence of fixed points in the voting flow. An unstable fixed point determines the critical threshold to full and total power. It can be varied from 50% up to 77% of initial support. Our model could shed new light on the last century eastern European communist collapse.

A new model of evolution is presented for finite size systems. Conditions under which a minority species can emerge, spread and stabilize to a macroscopic size are studied. It is found that space organization is instrumental in addition to a qualitative advantage. Some peculiar topologies ensure the overcome of the initial majority species. However the probability of such local clusters is very small and depend strongly on the system size. A probabilistic phase diagram is obtained for small sizes. It reduces to a trivial situation in the thermodynamic limit, thus indicating the importance of dealing with finite systems in evolution problems. Results are discussed with respect to both Darwin and punctuated equilibria theories.

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., Comment: Proceedings of the NATO Advanced Research Workshop, Budapest (May 1999) Eds: A. Gadomski et al

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., Comment: 10 pages, latex

This study extends classical models of spreading epidemics to describe the phenomenon of contagious public outrage, which eventually leads to the spread of violence following a disclosure of some unpopular political decisions and/or activity. Accordingly, a mathematical model is proposed to simulate from the start, the internal dynamics by which an external event is turned into internal violence within a population. Five kinds of agents are considered: "Upset" (U), "Violent" (V), "Sensitive" (S), "Immune" (I), and "Relaxed" (R), leading to a set of ordinary differential equations, which in turn yield the dynamics of spreading of each type of agents among the population. The process is stopped with the deactivation of the associated issue. Conditions coinciding with a twofold spreading of public violence are singled out. The results shed a new light to understand terror activity and provides some hint on how to curb the spreading of violence within population globally sensitive to specific world issues. Recent world violent events are discussed., Comment: 22 pages, 9 figures

Competing bimodal coalitions among a group of actors are discussed. First, a model from political sciences is revisited. Most of the model statements are found not to be contained in the model. Second, a new coalition model is built. It accounts for local versus global alignment with respect to the joining of a coalition. The existence of two competing world coaltions is found to yield one unique stable distribution of actors. On the opposite a unique world leadership allows the emergence of unstable relationships. In parallel to regular actors which have a clear coalition choice, ``neutral" ``frustrated" and ``risky" actors are produced. The cold war organisation after world war II is shown to be rather stable. The emergence of a fragmentation process from eastern group disappearance is explained as well as continuing western group stability. Some hints are obtained about possible policies to stabilize world nation relationships. European construction is analyzed with respect to european stability. Chinese stability is also discussed., 14 pages, latex, no figures, to appear in Physica A

The interplay between disorder and compressibility in Ising magnets is studied. Contrary to pure systems in which a weak compressibility drives the transition first order, we find from a renormalization group analysis that it has no effect on disordered systems which keep undergoing continuous transition with rigid random-bond Ising model critical exponents. The mean field calculation exhibits a dilution-dependent tricritical point beyond which, at stronger compressibility the transition is first order. The different behavior of XY and Heisenberg magnets is discussed., Comment: 16 pages, latex, 2 figures not included

We consider the phase diagram of two randomly coupled Ising models to mimic the successive phase transitions in plastic crystals. Detailed mean-field calculations are performed. Depending on the strength of the couplings, the phase diagrams display three ordered phases and some multicritical points. A tetracritical point is found to turn bicritical as the strength of the couplings increases. The nature of this multicritical point is then analyzed by means of a momentum-space renormalization-group calculation. Using the replica trick, we obtain an effective n-component spin Hamiltonian. The random coupling is found to be relevant and shown to have drastic effects on the multicritical behavior. The lower critical dimension is estimated to be ${\mathit{d}}_{\mathit{l}}$=2. In the n=0 limit, to first order in the parameter \ensuremath{\epsilon}=4-d, a system of seven recursion relations is obtained. Although there is a stable fixed point, it cannot be reached from physically acceptable initial conditions. We give arguments to support a runaway of the flow lines associated with a fluctuation-induced first-order transition.

It is found that a simple renormalization scheme may apply to spin glasses, provided time is added to real space coordinates among scaling variables. The model suggests that the critical slowing in spin glasses results not from a hierarchy but from a diffusion process among eigenstates available to the spin system in phase space.

Using a very simple renormalized site percolation model, the rich phase diagram exhibited by ACNxMn1−x mixtures, where A stands for K, Na or Rb while Mn represents Br, Cl or I, is obtained as function of cyanide concentration, x. From a steric hindrance argument, some cyanides are found to be randomly frozen at low temperatures being thus prevented from propagating long range orientational order. Actual cyanide density x should then be divided into a frozen-in part, xf, and a free-to-reorient part, xr, making only the last term relevant to quadrupolar ordering. The first term xf can indeed be calculated from microscopic characteristics of the molecules involved. This leads to the existence of two critical thresholds, xc and xd. While the former is associated to the disappearance of the ferroelastic transition, the latter defines the concentration extension range for the existence of ferroelastic domains. When available, experimental data for the critical thresholds are in excellent agreement with our calculated values. Predictions are made for a large variety of mixtures.

Financial economic models often assume that investors know (or agree on) the fundamental value of the shares of the firm, easing the passage from the individual to the collective dimension of the financial system generated by the Share Exchange over time. Our model relaxes that heroic assumption of one unique "true value" and deals with the formation of share market prices through the dynamic formation of individual and social opinions (or beliefs) based upon a fundamental signal of economic performance and position of the firm, the forecast revision by heterogeneous individual investors, and their social mood or sentiment about the ongoing state of the market pricing process. Market clearing price formation is then featured by individual and group dynamics that make its collective dimension irreducible to its individual level. This dynamic holistic approach can be applied to better understand the market exuberance generated by the Share Exchange over time., Comment: 22 pages, 9 figures

Public debates driven by incomplete scientific data where nobody can claim absolute certainty, due to current state of scientific knowledge, are studied. The cases of evolution theory, global warming and H1N1 pandemic influenza are investigated. The first two are of controversial impact while the third is more neutral and resolved. To adopt a cautious balanced attitude based on clear but inconclusive data appears to be a lose-out strategy. In contrast overstating arguments with wrong claims which cannot be scientifically refuted appear to be necessary but not sufficient to eventually win a public debate. The underlying key mechanism of these puzzling and unfortunate conclusions are identified using the Galam sequential probabilistic model of opinion dynamics. It reveals that the existence of inflexible agents and their respective proportions are the instrumental parameters to determine the faith of incomplete scientific data public debates. Acting on one's own inflexible proportion modifies the topology of the flow diagram, which in turn can make irrelevant initial supports. On the contrary focusing on open-minded agents may be useless given some topologies. When the evidence is not as strong as claimed, the inflexibles rather than the data are found to drive the opinion of the population. The results shed a new but disturbing light on designing adequate strategies to win a public debate., Comment: 31 pages, 7 figures

The 2-spin Ising model in statistical mechanics and the 2x2 normal form game in game theory are compared. All configurations allowed by the second are recovered by the first when the only concern is about Nash equilibria. But it holds no longer when Pareto optimum condiderations are introduced like in the prisoner's dilemma. This gap can nevertheless be filled by adding a new coupling term to the Ising model, even if that term has up to now no physical meaning. An individual complete bilinear objective function is thus found to be sufficient to reproduce all possible configurations of a 2x2 game. Using this one-to-one mapping, new perspectives for future research in both fields can be envisioned., 19 pages, no figure

We study the effect of inflexible agents on two state opinion dynamics. The model operates via repeated local updates of random grouping of agents. While floater agents do eventually flip their opinion to follow the local majority, inflexible agents keep their opinion always unchanged. It is a quenched individual opinion. In the bare model (no inflexibles), a separator at 50% drives the dynamics towards either one of two pure attractors, each associated with a full polarization along one of the opinions. The initial majority wins. The existence of inflexibles for only one of the two opinions is found to shift the separator at a lower value than 50% in favor of that side. Moreover it creates an incompressible minority around the inflexibles, one of the pure attractors becoming a mixed phase attractor. In addition above a threshold of 17% inflexibles make their side sure of winning whatever the initial conditions are. The inflexible minority wins. An equal presence of inflexibles on both sides restores the balanced dynamics with again a separator at 50% and now two mixed phase attractors on each side. Nevertheless, beyond 25% the dynamics is reversed with a unique attractor at a fifty-fifty stable equilibrium. But a very small advantage in inflexibles results in a decisive lowering of the separator at the advantage of the corresponding opinion. A few percent advantage does guarantee to become majority with one single attractor. The model is solved exhaustedly for groups of size 3., Comment: 18 pages, 12 figures

We apply a physical based model to describe the clothes fashion market. Every time a new outlet appears on the market, it can invade the market under certain specific conditions. Hence, the "old'' outlet can be completely dominated and disappears. Each creator competes for a finite population of agents. Fashion phenomena are shown to result from a collective phenomenon produced by local individual imitation effects. We assume that, in each step of the imitation process, agents only interact with a subset rather than with the whole set of agents. People are actually more likely to influence (and be influenced by) their close ''neighbours''. Accordingly we discuss which strategy is best fitted for new producers when people are either simply organised into anonymous reference groups or when they are organised in social groups hierarchically ordered. While counterfeits are shown to reinforce the first strategy, creating social leaders can permit to avoid them., 24 pages, 7 figures

We study how to restore site percolation on a damaged square lattice with nearest neighbor (N$^2$) interactions. Two strategies are suggested for a density $x$ of destroyed sites by a random attack at $p_c$. In the first one, a density $y$ of new sites are created with longer range interactions, either next nearest neighbor (N$^3$) or next next nearest neighbor (N$^4$). In the second one, new longer range interactions N$^3$ or N$^4$ are created for a fraction $v$ of the remaining $(p_c-x)$ sites in addition to their N$^2$ interactions. In both cases, the values of $y$ and $v$ are tuned in order to restore site percolation which then occurs at new percolation thresholds, respectively $\pi_3$, $\pi_4$, $\pi_{23}$ and $\pi_{24}$. Using Monte Carlo simulations the values of the pairs $\{y, \pi_3 \}$, $\{y, \pi_4\}$ and $\{v, \pi_{23}\}$, $\{v, \pi_{24}\}$ are calculated for the whole range $0\leq x \leq p_c(\text{N}^2)$. Our schemes are applicable to all regular lattices., Comment: 5 pages, revtex4

The September 11 attack on the US has revealed an unprecedented terrorism worldwide range of destruction. Recently, it has been related to the percolation of worldwide spread passive supporters. This scheme puts the suppression of the percolation effect as the major strategic issue in the fight against terrorism. Accordingly the world density of passive supporters should be reduced below the percolation threshold. In terms of solid policy, it means to neutralize millions of random passive supporters, which is contrary to ethics and out of any sound practical scheme. Given this impossibility we suggest instead a new strategic scheme to act directly on the value of the terrorism percolation threshold itself without harming the passive supporters. Accordingly we identify the space hosting the percolation phenomenon to be a multi-dimensional virtual social space which extends the ground earth surface to include the various independent terrorist-fighting goals. The associated percolating cluster is then found to create long-range ground connections to terrorism activity. We are thus able to modify the percolation threshold pc in the virtual space to reach p, Comment: 10 pages, 7 figures

Using a ferromagnetic Ising model, a new lattice homogeneity breaking approach (HBA) for two‐dimensional site dilution is presented. The critical temperature is stated to result from an energetic balance between the cluster center and its surface. This definition produces a breaking in the homogeneity of the system between the fluctuating cluster magnetization and the mean bulk counterpart. Site dilution is then found to generate additional breaking of the system homogeneity, with the introduction of a generalized surface effect which makes our procedure qualitatively different from the Bethe one. The HBA results in a simple new analytic expression for site percolation thresholds, which reproduces the exact values or numerical estimates for all lattice topologies in dimension two, within few percent.

Few years ago, application of the mean field Bethe scheme on a given system was shown to produce a systematic change of the system intrinsic symmetry. For instance, once applied on a ferromagnet, individual spins are no more equivalent. Accordingly a new loopwise mean field theory was designed to both go beyond the one site Weiss approach and yet preserve the initial Hamitonian symmetry. This loopwise scheme is applied here to solve the Triangular Antiferromagnetic Ising model. It is found to yield Wannier's exact result of no ordering at non-zero temperature. No adjustable parameter is used. Simultaneously a non-zero critical temperature is obtained for the Triangular Ising Ferromagnet. This simple mean field scheme opens a new way to tackle random systems., 14 pages, 2 figures

A model for terrorism is presented using the theory of percolation. Terrorism power is related to the spontaneous formation of random backbones of people who are sympathetic to terrorism but without being directly involved in it. They just don't oppose in case they could. In the past such friendly-to-terrorism backbones have been always existing but were of finite size and localized to a given geographical area. The September 11 terrorist attack on the US has revealed for the first time the existence of a world wide spread extension. It is argued to have result from a sudden world percolation of otherwise unconnected and dormant world spread backbones of passive supporters. The associated strategic question is then to determine if collecting ground information could have predict and thus avoid such a transition. Our results show the answer is no, voiding the major criticism against intelligence services. To conclude the impact of military action is discussed., Comment: 12 pages, 4 figures

The dynamics of spreading of the minority opinion in public debates (a reform proposal, a behavior change, a military retaliation) is studied using a diffusion reaction model. People move by discrete step on a landscape of random geometry shaped by social life (offices, houses, bars, and restaurants). A perfect world is considered with no advantage to the minority. A one person-one argument principle is applied to determine locally individual mind changes. In case of equality, a collective doubt is evoked which in turn favors the Status Quo.Starting from a large in favor of the proposal initial majority, repeated random size local discussions are found to drive the majority reversal along the minority hostile view. Total opinion refusal is completed within few days. Recent national collective issues are revisited. The model may apply to rumor and fear propagation., Comment: 11 pages, 2 figures

We discuss a cellular automata model to study the competition between an emergent better fitted species against an existing majority species. The model implement local fights among small group of individual and a synchronous random walk on a 2D lattice. The faith of the system, i.e. the spreading or disappearance of the species is determined by their initial density and fight frequency. The initial density of the emergent species has to be higher than a critical threshold for total spreading but this value depends in a non-trivial way of the fight frequency. Below the threshold any better adapted species disappears showing that a qualitative advantage is not enough for a minority to win. No strategy is involved but spatial organization turns out to be crucial. For instance at minority densities of zero measure some very rare local geometries which occur by chance are found to be killer geometries. Once set they lead with high probability to the total destruction of the preexisting majority species. The occurrence rate of these killer geometries is function of the system size. This model may apply to a large spectrum of competing groups like smoker-non smoker, opinion forming, diffusion of innovation setting of industrial standards, species evolution, epidemic spreading and cancer growth., Comment: 11 pages, 8 figures

International audience; Some universal features are independent of both the social nature of the individuals making the decision and the nature of the decision itself. On this basis a simple magnet like model is built. Pair interactions are introduced to measure the degree of exchange among individuals while discussing. An external uniform field is included to account for a possible pressure from outside. Individual biases with respect to the issue at stake are also included using local random fields. A unique postulate of minimum conflict is assumed. The model is then solved with emphasis on its psycho-sociological implications. Counter-intuitive results are obtained. At this stage no new physical technicality is involved. Instead the full psycho-sociological implications of the model are drawn. Few cases are then detailed to enlight them. In addition, several numerical experiments based on our model are shown to give both an insight on the dynamics of the model and suggest further research directions.

Percolation and jamming phenomena are investigated for random sequential deposition of rectangular needles on $d=2$ square lattices. Associated thresholds $p_c^{perc}$ and $p_c^{jam}$ are determined for various needle sizes. Their ratios $p_c^{perc} / p_c^{jam}$ are found to be a constant $0.62 \pm 0.01$ for all sizes. In addition the ratio of jamming thresholds for respectively square blocks and needles is also found to be a constant $0.79 \pm 0.01$. These constants exhibit some universal connexion in the geometry of jamming and percolation for both anisotropic shapes (needles versus square lattices) and isotropic shapes (square blocks on square lattices). A universal empirical law is proposed for all three thresholds as a function of $a$., 9 pages, latex, 4 eps figures included

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., Comment: 14 pages, to appear in EPJ B

Etude d'un modele de spin compressible avec deux especes differentes de variables de spin sur chaque site du reseau. L'integration des degres de liberte elastiques produit des couplages biquadratiques mixtes en plus des termes tetralineaires usuels. On considere trois voies differentes pour rendre compte des vibrations du reseau et discuter de la survenance des transitions du premier ordre. Analyse des resultats dans le contexte des cristaux plastiques

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}=\delta/d where a_s, a_b and \delta are 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., Comment: 11 pages, latex, 1 figure included

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., 7 pages, latex, 2 figures included

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., 25 pages, latex

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., Comment: 6 pages, latex, 2 figures not included. To appear in Physica A

The full phase diagram of K(CN)~Bri _~ mixtures is obtained using a mean-field treatment of a dilute random anharmonic compressible ferroelastic model. Integration of elastic degrees of freedom leads to a non-linear percolating problem. No random competing interactions are found. In parallel a simple linear hypothesis for an effective density of cyanides is assumed to account for the asymmetric shape of the cyanide versus the spherical bromide shape. Site percolation of cyanides is thus discriminated from the corresponding orientational percolation. Three characteristic values of cyanide concentration x = 0.2, 0.5 and 0.6 are obtained. For x < 0.6 the ferroelastic transition is lost. In the range 0.5 < x < 0.6, at low temperatures, cyanides form ferroelastic domains with random orientations. When 0.2 < x < 0.5 a collective dynamical glass is obtained. It tums to a single ion state for x < 0.2. It is then shown that the corresponding phase diagram of K~(Naj ~)CN mixtures is of a different physical nature. It involves in particular random competing interactions. A critical review of the orientational random field model is presented. The results are found to provide a unified and consistent framework to various experimental data. 1196 JOURNAL DE PHYSIQUE I M 8

A new model is presented to describe the low temperature part of the phase diagram of M(CN)xX1−x mixed crystals. The ferroelastic transition is lost at some threshold value xc greater than the percolation threshold pc. Between xc and pc no phase transition occurs. However, cyanides are found to form ferroelastic domains with random orientations generated by local static strains. These results are consistent with molecular dynamics calculations and supported by very recent shear torque experiments.

A simple Ising-like model is presented to describe the phase diagram of plastic crystals. In addition to a bilinear coupling between translations and rotations a reorientation-translation coupling is introduced via random fields which couple solely to rotational degrees of freedom. The physical basis of the reorientation-translation coupling is discussed using the rotational state hypothesis. The present approach is found to be consistent with some recent neutron experiments.

Mean field treatment of the dilute Ising antiferromagnet in a field is discussed. It is shown that to consider one average single magnetization does indeed account for the staggered symmetry of the model by including implicitly the effects of next nearest neighbor interactions which are not present in the initial Hamiltonian. The dependence of the equation of state on the dilution concentration is also discussed.

A new mechanism to explain the first order ferroelastic—ferroelectric transition in Terbium Molybdate (TMO) is presented. From group theory analysis it is shown that in the two-dimensional parameter space ordering along either an axis or a diagonal is forbidden. These symmetry-imposed singularities are found to make the unique stable fixed point not accessible for TMO. A continuous transition even if allowed within Landau theory is thus impossible once fluctuations are included. The TMO transition is therefore always first order. This explanation is supported by experimental results.

A new description of the coupling between translational and rotational degrees of freedom in plastic crystals is presented. Using the lattice-gas variable {ti} for translations and the q-state Potts variable {ri} for rotations a tetralinear coupling tiritjrj is introduced between nearest neighbours. Moreover, ionic crystals and molecular crystals are found to be described by different Hamiltonians. Random fields which couple solely to the {ri} are involved in the molecular case. The corresponding phase diagrams are obtained. The results are discussed with respect to experiments.