Related papers: Dynamics of Influence on Hierarchical Structures
Periodicity is one of the most fundamental structural characteristics of systems occurring in nature. The properties of these systems depend strongly on the symmetry of the underlying periodic structure. In solid state materials - for…
We have studied an evolutionary prisoner's dilemma game with players located on two types of random regular graphs with a degree of 4. The analysis is focused on the effects of payoffs and noise (temperature) on the maintenance of…
Many complex systems can be represented as networks of dynamical elements whose states evolve in response to interactions with neighboring elements, noise and external stimuli. The collective behavior of such systems can exhibit remarkable…
Simple nonlinear dynamical systems with multiple stable stationary states are often taken as models for switchlike biological systems. This paper considers the interaction of multiple such simple multistable systems when they are embedded…
We consider statistical-mechanical models for spin systems built on hierarchical structures, which provide a simple example of non-mean-field framework. We show that the coupling decay with spin distance can give rise to peculiar features…
We investigate the long-time behavior of a majority rule opinion dynamics model in finite spatial dimensions. Each site of the system is endowed with a two-state spin variable that evolves by majority rule. In a single update event, a group…
The density of states of disordered hopping models generically exhibits an essential singularity around the edges of its support, known as a Lifshitz tail. We study this phenomenon on the Bethe lattice, i.e. for the large-size limit of…
We investigate the competition between attractive spin-spin interactions and spin-separating external forces in the ground state of a one-dimensional Fermi-Hubbard model. We consider a lattice with open boundary conditions, subject to a…
We cast the metabolism of interacting cells within a statistical mechanics framework considering both, the actual phenotypic capacities of each cell and its interaction with its neighbors. Reaction fluxes will be the components of…
The behavior of the network and its stability are governed by both dynamics of individual nodes as well as their topological interconnections. Attention mechanism as an integral part of neural network models was initially designed for…
Synchronization has been the subject of intense research during decades mainly focused on determining the structural and dynamical conditions driving a set of interacting units to a coherent state globally stable. However, little attention…
In an extremely influential paper Mezard and Parisi put forward an analytic but non-rigorous approach called the cavity method for studying spin systems on the Bethe lattice, i.e., the random $d$-regular graph [Eur. Phys. J. B 20 (2001)…
We study quantum mechanical systems with "spin"-related contact interactions in one dimension. The boundary conditions describing the contact interactions are dependent on the spin states of the particles. In particular we investigate the…
We study a competition dynamics, based on the minority game, endowed with various substrate network structures. We observe the effects of the network topologies by investigating the volatility of the system and the structure of follower…
Pyrochlore magnets have proven to provide an excellent arena for the realization of a variety of many-body phenomena such as classical and quantum order-by-disorder, as well as spin liquid phases described by emergent gauge field theories.…
We establish long-range order for discrete nearest-neighbor spin systems on $\mathbb{Z}^d$ satisfying a certain symmetry assumption, when the dimension $d$ is higher than an explicitly described threshold. The results characterize all…
Low-dimensional quantum spin systems are interacting many body systems for which several rigorous results are known. Powerful techniques like the Bethe Ansatz provide exact knowledge of the ground state energy and low-lying excitation…
The dynamical process of opinion formation within a model using a local majority opinion updating rule is studied numerically in networks with the small-world geometrical property. The network is one in which shortcuts are added to randomly…
We found that the differential topology of the lattice-system of Ising model determines whether there can be the continuous phase transition, the geometric topology of the space the lattice-system is embedded in determines whether the…
We examine the ordering, pinning, and dynamics of two-dimensional pattern forming systems interacting with a periodic one-dimensional substrate. In the absence of the substrate, particles with competing long-range repulsion and short-range…