Related papers: Revisiting a Low-Dimensional Model with Short Rang…
The approach to equilibrium, from a nonequilibrium initial state, in a system at its critical point is usually described by a scaling theory with a single growing length scale, $\xi(t) \sim t^{1/z}$, where z is the dynamic exponent that…
A non-perturbative Renormalization Group approach is used to calculate scaling functions for an O(4) model in d=3 dimensions in the presence of an external symmetry-breaking field. These scaling functions are important for the analysis of…
We analyze numerically three different models exhibiting an absorbing phase transition. We focus on the finite-size scaling as well as the dynamical scaling behavior. An accurate determination of several critical exponents allows to…
We develop theoretical diagnostics for the breakdown of mean-field theory, demonstrate how spatial structure and finite interaction ranges enter the effective description, and show how these scales qualitatively modify the…
Complex interactions leading to phase transitions continue to hold a due interest in the scientific community. We charactersize a phase transition in a coupled oscillators model where interactions are not local in nature. At a first order…
The critical behavior of a quenched random hypercubic sample of linear size $L$ is considered, within the ``random-$T_{c}$'' field-theoretical mode, by using the renormalization group method. A finite-size scaling behavior is established…
In the 1960's, four famous scaling relations were developed which relate the six standard critical exponents describing continuous phase transitions in the thermodynamic limit of statistical physics models. They are well understood at a…
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…
Out-of-equilibrium quasistationary states (QSSs) are one of the signatures of a broken ergodicity in long-range interacting systems. For the widely studied Hamiltonian Mean-Field model, the lifetime of some QSSs has been shown to diverge…
We study the critical behavior and phase diagram of the $d$-dimensional random field O(N) model by means of the nonperturbative functional renormalization group approach presented in the preceding paper. We show that the dimensional…
A system defined by two coupled Ising models, with a bimodal random field acting in one of them, is investigated. The interactions among variables of each Ising system are infinite-ranged, a limit where mean field becomes exact. This model…
New theoretical and numerical analysis of the one-dimensional contact process with quenched disorder are presented. We derive new scaling relations, different from their counterparts in the pure model, which are valid not only at the…
We study a neural network model of interacting stochastic discrete two--state cellular automata on a regular lattice. The system is externally tuned to a critical point which varies with the degree of stochasticity (or the effective…
In this work we consider the universal crossover behavior of two non-equilibrium systems exhibiting a continuous phase transition. Focusing on the field driven crossover from mean-field to non-mean-field scaling behavior we show that the…
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…
The most general form of a marginal extended perturbation in a two-dimensional system is deduced from scaling considerations. It includes as particular cases extended perturbations decaying either from a surface, a line or a point for which…
We restrict our computation in the mean field approximation which could lead to a clear critical behavior. We analyze the scaling behavior with different shape of interaction kernel by considering different dressed-gluon models. The…
We study the two-dimensional kinetic Ising model below its equilibrium critical temperature, subject to a square-wave oscillating external field. We focus on the multi-droplet regime where the metastable phase decays through nucleation and…
Quasistationary states are long-lived nonequilibrium states, observed in some systems with long-range interactions under deterministic Hamiltonian evolution. These intriguing non-Boltzmann states relax to equilibrium over times which…
An introductory review to short-time critical dynamics is given. From the scaling relation valid already in the early stage of the evolution of a system at or near the critical point, one derives power law behaviour for various quantities.…