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We compare phase transition and critical phenomena of bond percolation on Euclidean lattices, nonamenable graphs, and complex networks. On a Euclidean lattice, percolation shows a phase transition between the nonpercolating phase and…
Co-evolution exhibited by a network system, involving the intricate interplay between the dynamics of the network itself and the subsystems connected by it, is a key concept for understanding the self-organized, flexible nature of…
Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…
The study of random graphs has become very popular for real-life network modeling such as social networks or financial networks. Inhomogeneous long-range percolation (or scale-free percolation) on the lattice $\mathbb Z^d$, $d\ge1$, is a…
In this paper we study a simple model of a purely excitatory neural network that, by construction, operates at a critical point. This model allows us to consider various markers of criticality and illustrate how they should perform in a…
If we add links to a network at random, a critical threshold can be crossed where a giant connected component forms. Conversely, if links or nodes are removed at random, the giant component shrinks and eventually breaks. In this paper, we…
Friction is a phenomenon that manifests across all spatial and temporal scales, from the molecular to the macroscopic scale. It describes the dissipation of energy from the motion of particles or abstract reaction coordinates and arises in…
Criticality has been proposed as a mechanism for the emergence of complexity, life, and computation, as it exhibits a balance between robustness and adaptability. In classic models of complex systems where structure and dynamics are…
Nonequilibrium phenomena of the phase transitions are studied. It is shown that due to finite relaxation time of the particle distributions, the use of scalar background dependent distribution functions is inconsistent.This observation may…
Scale invariance profoundly influences the dynamics and structure of complex systems, spanning from critical phenomena to network architecture. Here, we propose a precise definition of scale-invariant networks by leveraging the concept of a…
DNA denaturation, wetting in two dimensions, depinning of a flux line, and other problems map onto a phase transition with effective long range interaction. It yields giant non-universal critical indexes, arbitrarily large macroscopic…
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…
We suggest a model for data losses in a single node of a packet-switched network (like the Internet) which reduces to one-dimensional discrete random walks with unusual boundary conditions. The model shows critical behavior with an abrupt…
Small changes in an external parameter can often lead to dramatic qualitative changes in the lowest energy quantum mechanical ground state of a correlated electron system. In anisotropic crystals, such as the high temperature…
In self-organized criticality (SOC) models, as well as in standard phase transitions, criticality is only present for vanishing external fields $h \to 0$. Considering that this is rarely the case for natural systems, such a restriction…
Disordered fibrous networks are ubiquitous in nature as major structural components of living cells and tissues. The mechanical stability of networks generally depends on the degree of connectivity: only when the average number of…
We discuss reservoir induced phase transitions of lattice fermions in the non-equilibrium steady state (NESS) of an open system with local reservoirs. These systems may become critical in the sense of a diverging correlation length upon…
The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same…
The observation of apparent power-laws in neuronal systems has led to the suggestion that the brain is at, or close to, a critical state and may be a self-organised critical system. Within the framework of self-organised criticality a…
Inspired by dengue and yellow fever epidemics, we investigated the contact process (CP) in a multiscale network constituted by one-dimensional chains connected through a Barab\'asi-Albert scale-free network. In addition to the CP dynamics…