The aim of this work is to implement a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. A class of simple mean-field discrete models is introduced and discussed both from the theoretical and phenomenological point of view. We propose a parameter evaluation procedure and test it by fitting the model against three families of data coming from different cases: the estimated interaction parameters are found to have similar positive values, giving a quantitative confirmation of the peer imitation behavior found in social psychology. Furthermore, all the values of the interaction parameters belong to the phase transition regime suggesting its possible role in the study of social systems

A new mean field statistical mechanics model of two interacting groups of spins is introduced and the phase transition studied in terms of their relative size. A jump of the average magnetization is found for large values of the mutual interaction when the relative percentage of the two populations crosses a critical threshold.It is shown how the critical percentage depends on internal interactions and on the initial magnetizations. The model is interpreted as a prototype of residentimmigrant cultural interaction and conclusions from the social sciences perspectives are drawn. IntroductionIn the last few decades the statistical mechanics approach has seen an impressive expansion in fields as diverse as combinatorial optimization, finance, biology and others. Its success relies upon the fact that every problem of many interacting parts may be studied by its methods and techniques. Our plan in this work is to introduce a statistical mechanics model with the purpose of describing two homogeneous groups of individuals whose interaction is imitative within the same group but may be imitative or counter-imitative between different groups. Such a model may represent a first attempt toward the construction of a statistical mechanics theory of the phenomenon of cultural interchange. When 1 two populations come in contact, like in the case of immigration but also in a more general context through the media, it is often seen how cultural traits are sometimes mixed, while some other times one of the two dominates and prevails on the other. Examples are found in linguistics, as well as in opinion forming dynamics ([1], [2], [3]). One interesting feature of those changes is that sometimes they appear to be smoothly varying with the relative proportions of the two groups, some other times the crossing of a critical value triggers a jump of the observed quantity [4]. What we are building here is the mean field theory of the two population problem i.e. we consider every individual interacting with every other with the same strength. In future works we plan to introduce a more realistic model by allowing randomness of the interaction strength like in the Sherrington-Kirkpatrick spin glass model ([5] [6]) and also a more structured network connection like, for instance, the one predicted by the small-world theory [7] [8]. We want to stress that, although our model is inspired by the Curie-Weiss theory of ferromagnetism, the problem we deal with here is quite different because we do not study the phase transition in terms of the temperature but in terms of the relative size of the two populations.The dictionary we plan to follow is easily explained by saying that a cultural trait is considered for simplicity as a dichotomic variable σ i = ±1. The interaction between particles is built up as a sum of pairwise interactions and plays the role of cultural interaction between two individuals i and j as described by a potential, or a cost function, which simply reflects the will to "agree" or "disagree" among the two. The two at...

Modern societies feature an increasing contact between cultures, yet we have a poor understanding of what the outcomes might be. Here we consider a mathematical model of contact between social groups, grounded in social psychology and analyzed using tools from statistical physics. We use the model to study how a culture might be affected by immigration. We find that in some cases residents' culture is relatively unchanged, but in other cases residents may adopt the opinions and beliefs of immigrants. The decisive factors are each group's cultural legacy and its attitudes towards in-and out-groups. The model can also predict how social policies may influence the outcome of culture contact.

This paper shows that differentiating the lifetimes of two phenotypes independently from their fertility can lead to a qualitative change in the equilibrium of a population: since survival and reproduction are distinct functional aspects of an organism, this observation contributes to extend the population-genetical characterisation of biological function. To support this statement a mathematical relation is derived to link the lifetime ratio T₁/T₂, which parameterizes the different survival ability of two phenotypes, with population variables that quantify the amount of neutral variation underlying a population's phenotypic distribution.

Promoting and increasing energy efficiency is a promising method of reducing CO 2 emissions and avoiding the potentially devastating effects of climate change. The question is: How do we induce a cultural or behavioural change whereby people nationally and globally adopt more energy efficient lifestyles?We propose a new family of mathematical models, based on a statistical mechanics extension of discrete choice theory, that offer a set of formal tools to systematically analyse and quantify this problem. An application example could be to predict the percentage of people choosing to buy new energy efficient light bulbs instead of the traditional incandescent versions. Through statistical evaluation of survey responses, the models can identify the key driving factors in the decision-making process; for example, the extent to which people imitate each other. These models allow us to incorporate the effect of social interactions could help us identify 'tipping points' at a societal level. This knowledge could be used to trigger structural changes in our society. The results may provide tangible and deliverable evidence-based policy options to decision-makers.We believe that these models offer an opportunity for the research community-in both the social and physical sciences-and decision-makers in the private and public sectors to work together towards preventing the potentially devastating social, economic and environmental effects of climate change.