Related papers: Higher-order Ising model on hypergraphs
Modeling social systems as networks based on pairwise interactions between individuals offers valuable insights into the mechanisms underlying their dynamics. However, the majority of social interactions occur within groups of individuals,…
We study the non-equilibrium phase diagram of a fully-connected Ising $p$-spin model, for generic $p>2$, and investigate its robustness with respect to the inclusion of spin-wave fluctuations, resulting from a ferromagnetic, short-range…
We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of…
The one-dimensional extended isotropic XY model (s=1/2) in a transverse field with uniform long-range interactions among the \textit{z} components of the spin is considered. The model is exactly solved by introducing the gaussian and…
We briefly introduce hysteresis in spatially extended systems and the dynamic phase transition observed as the frequency of the oscillating field increases beyond a critical value. Hysteresis and the decay of metastable phases are closely…
The $2$d orders are a sub class of causal sets, which is especially amenable to computer simulations. Past work has shown that the $2$d orders have a first order phase transition between a random and a crystalline phase. When coupling the…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…
Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for…
We analyse biased ensembles of trajectories for the random-field Ising model on a fully-connected lattice, which is described exactly by mean-field theory. By coupling the activity of the system to a dynamical biasing field, we find a range…
Recent studies have investigated various dynamic processes characterizing collective behaviors in real-world systems. However, these dynamics have been studied individually in specific contexts. In this article, we present a holistic…
The Ising model provides a natural mapping for many computationally hard combinatorial optimization problems (COPs). Consequently, dynamical system-inspired computing models and hardware platforms that minimize the Ising Hamiltonian, have…
We live and cooperate in networks. However, links in networks only allow for pairwise interactions, thus making the framework suitable for dyadic games, but not for games that are played in groups of more than two players. Here, we study…
Collective decision-making is a widespread phenomenon in both biological and artificial systems, where individuals reach a consensus through social interactions. While traditional models of opinion dynamics and contagion focus on pairwise…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…
While the equilibrium properties, states, and phase transitions of interacting systems are well described by statistical mechanics, the lack of suitable state parameters has hindered the understanding of non-equilibrium phenomena in diverse…
Complex systems exhibit macroscopic behaviors that emerge from the coordinated interactions of their individual components. Understanding the microscopic origins of these emergent properties remains a significant challenge, especially in…
Hypergraphs effectively model higher-order relationships in natural phenomena, capturing complex interactions beyond pairwise connections. We introduce a novel hypergraph message passing framework inspired by interacting particle systems,…
Animal communication is frequently studied with conventional network representations that link pairs of individuals who interact, for example, through vocalisation. However, acoustic signals often have multiple simultaneous receivers, or…
Human behaviors in social systems are often shaped by group pressure and collective norms, especially since the rise of social media platforms. However, in the context of adopting misbehaviors, most existing contagion models rely on…
In this paper we consider an approach, which allows researching a processes of order-disorder transition in various systems (with any distribution of the exchange integrals signs) in the frame of Ising model. A new order parameters, which…