Related papers: Why everything gets slower ?
The ferromagnetic Ising model on an $n\times n$ square lattice region $\Lambda$ with mixed boundary conditions can exhibit a phase transition as temperature varies. For this spin system, if we fix the spins on the top and bottom sides of…
We develop a mathematical model to describe the persistence of rule-breaking behaviors in societies, such as traffic violations, disregard for legal restrictions and other forms of noncompliance. Using a replicator-type dynamics with…
A theoretical model is presented which provides a way to simulate, at a very abstract level, power struggles in the social world. In the model, agents can benefit or harm each other, to varying degrees and with differing levels of…
Although classical economic theory is based on the concept of stable equilibrium, real economic systems appear to be always out of equilibrium. Indeed, they share many of the dynamical features of other complex systems, e.g., ecological…
Most instruments - formalisms, concepts, and metrics - for social networks analysis fail to capture their dynamics. Typical systems exhibit different scales of dynamics, ranging from the fine-grain dynamics of interactions (which recently…
In this work we review some recent development in the mathematical modelling of quantitative sociology by means of statistical mechanics. After a short pedagogical introduction to static and dynamic properties of many body systems, we…
The Heider balance (HB) is investigated in a fully connected graph of $N$ nodes. The links are described by a real symmetric array r(i,j), i,j=1,...,N. In a social group, nodes represent group members and links represent relations between…
We study the evolution of social clusters, in an analogy with physical spin systems, and in detail show the importance of the concept of the "self" of each agent with quantifiable variable attributes. We investigate the effective influence…
A microscopic approach to macroeconomic features is intended. A model for macroeconomic behavior based on the Ausloos-Clippe-Pekalski model is built and investigated. The influence of a discrete time information transfer is investigated.…
Slow-roll inflation generically makes several predictions: a flat Universe, primordial adiabatic density perturbations, and a stochastic gravity-wave background. Each inflation model will further predict specific relations between the…
A kinetic one-dimensional Ising model on a ring evolves according to a generalization of Glauber rates, such that spins at even (odd) lattice sites experience a temperature $T_{e}$ ($T_{o}$). Detailed balance is violated so that the spin…
A clear separation of the time scales governing the dynamics of "slow" and "fast" degrees of freedom often serves as a prerequisite for the emergence of an independent low-energy theory. Here, we consider (slow) classical spins exchange…
The Anthropocene is characterized by close interdependencies between the natural Earth system and the human society, posing novel challenges to model development. Here we present a conceptual model describing the long-term coevolution of…
Kob and Andersen's simple lattice models for the dynamics of structural glasses are analyzed. Although the particles have only hard core interactions, the imposed constraint that they cannot move if surrounded by too many others causes slow…
After a sudden disruption, weakly interacting quantum systems first relax to a prethermalized state that can be described by perturbation theory and a generalized Gibbs ensemble. Using these properties of the prethermalized state we…
We demonstrate that the Ising all-to-all (ATA) model exhibits a range of dynamics, from integrable to chaotic, including mixed behaviour across symmetry blocks within a single system. While other works have explored the dynamics of…
Recent attempts to understand the origin of social fragmentation are based on spin models which include terms accounting for two social phenomena: homophily -- the tendency for people with similar opinions to establish positive relations --…
Emergence of hierarchies is investigated by Monte Carlo simulation in a timid society where all individuals are pacifist. The self-organiztion of hierarchies is shown to occur in two steps as the population is increased, i.e. there are…
A zero temperature dynamics of Ising spin glasses and ferromagnets on random graphs of finite connectivity is considered, like granular media these systems have an extensive entropy of metastable states. We consider the problem of what…
Scaling has been proposed as a powerful tool to analyze the properties of complex systems, and in particular for cities where it describes how various properties change with population. The empirical study of scaling on a wide range of…