Related papers: A simple mean field model for social interactions:…
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…
We consider a system of hierarchical interacting spins under dynamics of spin-flip type with a ferromagnetic mean field interaction, scaling with the hierarchical distance, coupled with a system of linearly interacting hierarchical…
Facilitated spin models on random graphs provide an ideal microscopic realization of the mode-coupling theory of supercooled liquids: they undergo a purely dynamic glass transition with no thermodynamic singularity. In this paper we study…
We have numerically investigated the mean-field dynamics of the the $p$-spin interaction spin glass model with p=3 using an efficient method of integrating the dynamic equations. We find a new time scale associated with the onset of the…
We study the critical behavior of a general contagion model where nodes are either active (e.g. with opinion A, or functioning) or inactive (e.g. with opinion B, or damaged). The transitions between these two states are determined by (i)…
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…
In a class of heterogeneous random networks, where each node dynamics is a random dynamical system, interacting with neighbor nodes via a random coupling function, we characterize the hub behavior as the mean-field, subject to statistically…
Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game…
A cellular automaton model is presented for random walkers with biologically motivated interactions favoring local alignment and leading to collective motion or swarming behavior. The degree of alignment is controlled by a sensitivity…
In all local low-dimensional models, scaling at critical points deviates from mean field behavior -- with one possible exception. This exceptional model with ``ordinary" behavior is an inherently non-equilibrium model studied some time ago…
Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…
Mean-field models of glasses that present a random first order transition exhibit highly non-trivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for…
We consider the dynamics of a diluted mean-field spin glass model in the aging regime. The model presents a particularly rich heterogeneous behavior. In order to catch this behavior, we perform a **spin-by-spin analysis** for a **given…
Simple elastic models of spin-crossover compounds are known empirically to exhibit classical critical behavior. We demonstrate how the long-ranged interactions responsible for this behavior arise naturally upon integrating out mechanical…
We study the dynamics of fluctuations at the critical point for two time-asymmetric version of the Curie-Weiss model for spin systems that, in the macroscopic limit, undergo a Hopf bifurcation. The fluctuations around the macroscopic limit…
A model of interacting random walkers is presented and shown to give rise to patterns consisting in periodic arrangements of fluctuating particle clusters. The model represents biological individuals that die or reproduce at rates depending…
We develop a theory of fluctuations for Brownian systems with weak long-range interactions. For these systems, there exists a critical point separating a homogeneous phase from an inhomogeneous phase. Starting from the stochastic…
Symmetries represent a fundamental constraint for physical systems and relevant new phenomena often emerge as a consequence of their breaking. An important example is provided by space- and time-translational invariance in statistical…
The processes of interplant competition within a field are still poorly understood. However, they explain a large part of the heterogeneity in a field and may have longer-term consequences, especially in mixed stands. Modeling can help to…
We perform simulations for one dimensional continuous-time random walks in two dynamic random environments with fast (independent spin-flips) and slow (simple symmetric exclusion) decay of space-time correlations, respectively. We focus on…