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Many social, biological, and economic systems can be approached by complex networks of interacting units. The behaviour of several models on small-world networks has recently been studied. These models are expected to capture the essential…
A fundamental problem of out-of-equilibrium physics is the speed at which the order parameter grows upon crossing a phase transition. Here, we investigate the dynamics of ordering in a Fermi gas undergoing a density-wave phase transition…
Long-range interacting systems may exhibit ensemble inequivalence and can possibly attain equilibrium states under completely open conditions, for which energy, volume and number of particles simultaneously fluctuate. Here we consider a…
In the present chapter we study the emergence of global patterns in large groups in first and second-order multi-agent systems, focusing on two ingredients that influence the dynamics: the interaction network and the state space. The state…
Diverse equilibrium systems with heterogeneous interactions lie at the edge of stability. Such marginally stable states are dynamically selected as the most abundant ones or as those with the largest basins of attraction. On the other hand,…
Non-equilibrium systems lack an explicit characterisation of their steady state like the Boltzmann distribution for equilibrium systems. This has drastic consequences for the inference of parameters of a model when its dynamics lacks…
Self-propelled particles with anti-aligning interactions generally do not form a polar order. However, in this Letter, we show that when multiple types of such particles coexist and interact through aligning interactions between different…
We introduce a three-state model to study the effects of a neutral party on opinion spreading, in which the tendency of agents to agree with their neighbors can be tuned to favor either the neutral party or two oppositely polarized parties,…
A two species particle model on an open chain with dynamics which is non-conserving in the bulk is introduced. The dynamical rules which define the model obey a symmetry between the two species. The model exhibits a rich behavior which…
Nonreciprocal interactions in many-body systems lead to time-dependent states, commonly observed in biological, chemical, and ecological systems. The stability of these states in the thermodynamic limit and the critical behavior of the…
In this work, we employed Monte Carlo simulations to study the Ising, $XY$, and Heisenberg models on a simple cubic lattice, where the system models evolve toward the steady state under the influence of competition between one- and two-spin…
Models of the convergence of opinion in social systems have been the subject of a considerable amount of recent attention in the physics literature. These models divide into two classes, those in which individuals form their beliefs based…
Out of equilibrium, the lack of reciprocity is the rule rather than the exception. Non-reciprocal interactions occur, for instance, in networks of neurons, directional growth of interfaces, and synthetic active materials. While wave…
We describe a phase transition that gives rise to structurally non-trivial states in a two-dimensional ordered network of particles connected by harmonic bonds. Monte Carlo simulations reveal that the network supports, apart from the…
Usually complex charge ordering phenomena arise due to competing interactions. We have studied how such ordered patterns emerge from the frustration of a long-ranged interaction on a lattice. Using the lattice gas model on a square lattice…
Competition between ordered phases, and their associated phase transitions, are significant in the study of strongly correlated systems. Here we examine one aspect, the nonequilibrium dynamics of a photoexcited Mott-Peierls system, using an…
We consider general properties of groups of interacting oscillators, for which the natural frequencies are not in resonance. Such groups interact via non-oscillating collective variables like the amplitudes of the order parameters defined…
We investigate global phase coherence in a system of coupled oscillators on a small-world networks constructed from a ring with nearest-neighbor edges. The effects of both thermal noise and quenched randomness on phase ordering are examined…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive…