Related papers: Griffiths phase emerging from strong mutualistic d…
We study the equilibria of a large Lokta-Volterra system of coupled differential equations in the case where the interaction coefficients form a large random matrix. In the case where this random matrix follows an elliptic model , we study…
Explaining the emergence of self-organized biodiversity and species abundance distribution patterns remians a fundamental challenge in ecology. While classical frameworks, such as neutral theory and models based on pairwise species…
Phase field evolutions are obtained by means of time discrete schemes, providing (or selecting) at each time step an equilibrium configuration of the system, which is usually computed by descent methods for the free energy (e.g.staggered…
The generalized Lotka-Volterra (GLV) equations with quenched random interactions have been extensively used to investigate the stability and dynamics of complex ecosystems. However, the standard linear interaction model suffers from…
How diversity is maintained in natural ecosystems is a long-standing question in Theoretical Ecology. By studying a system that combines ecological dynamics, heterogeneous interactions and spatial structure, we uncover a new mechanism for…
High-order interdependencies are central features of complex systems, yet a mechanistic explanation for their emergence remains elusive. Currently, it is unknown under what conditions high-order interdependencies, quantified by the…
Via the hierarchy of correlations, we study the Mott insulator phase of the Fermi-Hubbard model in the limit of strong interactions and derive a quantum Boltzmann equation describing its relaxation dynamics. In stark contrast to the weakly…
In this brief, we study epidemic spreading dynamics taking place in complex networks. We specifically investigate the effect of synergy, where multiple interactions between nodes result in a combined effect larger than the simple sum of…
We study an evolution cross-diffusion problem with mutualistic Lotka-Volterra reaction term to modelize the long-term spatial distribution of labor and capital. The mutualistic behavior is deduced from the gradient flow associated to…
Does an ecological community allow stable coexistence? Identifying the general principles that determine the answer to this question is a central problem of theoretical ecology. Random matrix theory approaches have uncovered the general…
The imbalanced Hubbard model features a transition between dynamic regimes depending on the mass ratio and coupling strength between two different particle species. A slowdown of the lighter particle transport can be attributed to an…
Topological phases of matter are defined by their nontrivial patterns of ground-state quantum entanglement, which is irremovable so long as the excitation gap and the protecting symmetries, if any, are maintained. Recent studies on…
We study the nonequilibrium phase transition in the two-dimensional contact process on a randomly diluted lattice by means of large-scale Monte-Carlo simulations for times up to $10^{10}$ and system sizes up to $8000 \times 8000$ sites. Our…
The Griffiths inequalities for Ising spin-glass models with Gaussian randomness of non-vanishing mean are proved using properties of the Gaussian distribution and gauge symmetry of the system. These inequalities imply that correlation…
A key notion in heavy-fermion systems is the entanglement between conduction electrons and localized spin degrees of freedom. To study these systems from this point of view, we compute the mutual information in a ferromagnetic and…
Molecular dynamics simulations of interacting soft disks confined in a heterogeneous quenched matrix of soft obstacles show dynamics which is fundamentally different from that of hard disks. The interactions between the disks can enhance…
A new type of collective excitations, due exclusively to the topology of a complex random network that can be characterized by a fractal dimension $D_F$, is investigated. We show analytically that these excitations generate phase…
In this paper, we investigate signatures of topological phase transitions in interacting systems. We show that the key signature is the existence of a topologically protected level crossing, which is robust and sharply defines the…
We propose a family of models to study the evolution of ties in a network of interacting agents by reinforcement and penalization of their connections according to certain local laws of interaction. The family of stochastic dynamical…
We analyze purely competitive many-species Lotka-Volterra systems with random interaction matrices, focusing the attention on statistical properties of their asymptotic states. Generic features of the evolution are outlined from a…