Related papers: Macroscopic cycles for the interchange and quantum…
A novel approach for studying phase transitions in systems with quantum degrees of freedom is discussed. Starting from the microscopic hamiltonian of a quantum model, we first derive a set of exact differential equations for the free energy…
We examine the number of cycles of length k in a permutation, as a function on the symmetric group. We write it explicitly as a combination of characters of irreducible representations. This allows to study formation of long cycles in the…
In the interchange process on a graph $G=(V,E)$, distinguished particles are placed on the vertices of $G$ with independent Poisson clocks on the edges. When the clock of an edge rings, the two particles on the two sides of the edge…
We introduce an elementary quantum system consisting of a set of spins on a graph and a particle hopping between its nodes. The quantum state is build sequentially, applying a unitary transformation that couples neighboring spins and, at a…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
The random-cluster model is a dependent percolation model that has applications in the study of Ising and Potts models. In this paper, several new results are obtained for the random-cluster model on nonamenable graphs with cluster…
We introduce a class of random graphs with a community structure, which we call the hierarchical configuration model. On the inter-community level, the graph is a configuration model, and on the intra-community level, every vertex in the…
While there has been tremendous activity in the area of statistical network inference on graphs, hypergraphs have not enjoyed the same attention, on account of their relative complexity and the lack of tractable statistical models. We…
We introduce a diagrammatic multi-scale approach to the Hubbard model based on the interaction-irreducible (multi-boson) vertex of a small cluster embedded in a self-consistent medium. The vertex captures short-ranged correlations up to the…
Transition graphs capture the memory and sequential response of multistable media, by specifying their evolution under external driving. Microscopically, collections of bistable elements, or hysterons, provide a powerful model for these…
Although ubiquitous, interactions of groups of individuals (e.g., modern messaging applications, group meetings, or even a parliament discussion) are not yet thoroughly studied. Frequently, single-groups are modeled as critical-mass…
The quantum switch is a higher-order operation that takes as an input two quantum processes and combines them in a coherent superposition of two alternative orders. Here we provide an approach to the quantum switch based on the methods of…
We propose a generic framework to describe classical Ising-like models defined on arbitrary graphs. The energy spectrum is shown to be the Hadamard transform of a suitably defined sparse "coding" vector associated with the graph. We expect…
We develop a generic method to compute the dynamics induced by quenches in completely connected quantum systems. These models are expected to provide a mean-field description at least of the short time dynamics of finite dimensional system.…
Quantum random walks represent a powerful tool for the implementation of various quantum algorithms. We consider a convolution problem for the graphs which provide quantum and classical random walks. We suggest a new method for lattices and…
Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…
The evolution of certain pair state in a quantum network with isomorphic branches, governed by the Heisenberg $XY$ Hamiltonian, depends solely on the local structure, and it remains unaffected even if the global structure is altered. All…
Most networks tend to show complex and multiple relationships between entities. Networks are usually modeled by graphs or hypergraphs; nonetheless a given entity can occur many times in a relationship: this brings the need to deal with…
We introduce a spatial graph and hypergraph model that smoothly interpolates between a graph with purely pairwise edges and a graph where all connections are in large hyperedges. The key component is a spatial clustering resolution…
Analysis of complex networks, particularly material networks such as the carbon skeleton of hydrocarbons generated in hydrocarbon pyrolysis in carbon-rich systems, is essential for effectively describing, modeling, and predicting their…