Related papers: Spin models on random graphs with controlled topol…
We present an analytical approach for describing spectrally constrained maximum entropy ensembles of finitely connected regular loopy graphs, valid in the regime of weak loop-loop interactions. We derive an expression for the leading two…
In this paper we study the maximum degree of interaction which may emerge in distributed systems. It is assumed that a distributed system is represented by a graph of nodes interacting over edges. Each node has some amount of data. The…
Quantum simulation of spin models can provide insight into complex problems that are difficult or impossible to study with classical computers. Trapped ions are an established platform for quantum simulation, but only systems with fewer…
In this work we study the dynamics of systems composed of numerous interacting elements interconnected through a random weighted directed graph, such as models of random neural networks. We develop an original theoretical approach based on…
We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the…
We propose an algorithm to obtain numerically approximate solutions of the direct Ising problem, that is, to compute the free energy and the equilibrium observables of spin systems with arbitrary two-spin interactions. To this purpose we…
We present a new method to close the Master Equation representing the continuous time dynamics of Ising interacting spins. The method makes use of the the theory of Random Point Processes to derive a master equation for local conditional…
In many areas such as computational biology, finance or social sciences, knowledge of an underlying graph explaining the interactions between agents is of paramount importance but still challenging. Considering that these interactions may…
We consider the Ising model for two interacting groups of spins embedded in an Erd\"{o}s-R\'{e}nyi random graph. The critical properties of the system are investigated by means of extensive Monte Carlo simulations. Our results evidence the…
Understanding the relationship between the heterogeneous structure of complex networks and cooperative phenomena occurring on them remains a key problem in network science. Mean-field theories of spin models on networks constitute a…
The known Pfaffian structure of the boundary spin correlations, and more generally order-disorder correlation functions, is given a new explanation through simple topological considerations within the model's random current representation.…
In a random graph, counts for the number of vertices with given degrees will typically be dependent. We show via a multivariate normal and a Poisson process approximation that, for graphs which have independent edges, with a possibly…
Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…
Numerical transfer-matrix methods are applied to two-dimensional Ising spin systems, in presence of a confining magnetic field which varies with distance $|{\vec x}|$ to a "trap center", proportionally to $(|{\vec x}|/\ell)^p$, $p>0$. On a…
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…
Random graph models have played a dominant role in the theoretical study of networked systems. The Poisson random graph of Erdos and Renyi, in particular, as well as the so-called configuration model, have served as the starting point for…
The finite size scaling behaviour for the Ising model in five dimensions, with either free or cyclic boundary, has been the subject for a long running debate. The older papers have been based on ideas from e.g. field theory or…
Facilitated or kinetically constrained spin models (KCSM) are a class of interacting particle systems reversible w.r.t. to a simple product measure. Each dynamical variable (spin) is re-sampled from its equilibrium distribution only if the…
We discuss two sampling schemes for selecting random subnets from a network: Random sampling and connectivity dependent sampling, and investigate how the degree distribution of a node in the network is affected by the two types of sampling.…
Round-based models are very common message-passing models; combinatorial topology applied to distributed computing provides sweeping results like general lower bounds. We combine both to study the computability of k-set agreement. Among all…