Related papers: Laplacian Renormalization Group: An introduction t…
The renormalization group is the cornerstone of the modern theory of universality and phase transitions, a powerful tool to scrutinize symmetries and organizational scales in dynamical systems. However, its network counterpart is…
Complex networks can model a range of different systems, from the human brain to social connections. Some of those networks have a large number of nodes and links, making it impractical to analyze them directly. One strategy to simplify…
The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling…
We propose a cross-order Laplacian renormalization group (X-LRG) scheme for arbitrary higher-order networks. The renormalization group is a pillar of the theory of scaling, scale-invariance, and universality in physics. An RG scheme based…
Diffusion over networks has recently been used to define spatiotemporal scales and extend Kadanoff block spins of Euclidean space to supernodes of networks in the Laplacian renormalization group (LRG). Yet, its ad hoc coarse-graining…
Exploring and understanding topological phases in systems with strong distributed disorder requires developing fundamentally new approaches to replace traditional tools such as topological band theory. Here, we present a general real-space…
Self-similarity, where observables at different length scales exhibit similar behavior, is ubiquitous in natural systems. Such systems are typically characterized by power-law correlations and universality, and are studied using the…
Heterogeneous and complex networks represent intertwined interactions between real-world elements or agents. Determining the multi-scale mesoscopic organization of clusters and intertwined structures is still a fundamental and open problem…
We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena…
Physical systems differring in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the…
At low energies, the microscopic characteristics and changes of physical systems as viewed at different distance scales are described by universal scale invariant properties investigated by the Renormalization Group (RG) apparatus, an…
The renormalization group (RG) is a class of theoretical techniques used to explain the collective physics of interacting, many-body systems. It has been suggested that the RG formalism may be useful in finding and interpreting emergent…
Renormalization group (RG) methods, which model the way in which the effective behavior of a system depends on the scale at which it is observed, are key to modern condensed-matter theory and particle physics. We compare the ideas behind…
We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Kenneth…
The renormalization group (RG) is an essential technique in statistical physics and quantum field theory, which considers scale-invariant properties of physical theories and how these theories' parameters change with scaling. Deep learning…
In this thesis we investigate the Renormalization Group (RG) approach in finite-dimensional glassy systems, whose critical features are still not well-established, or simply unknown. We focus on spin and structural-glass models built on…
We analyze the renormalization-group (RG) flows of two effective Lagrangians, one for measurement induced transitions of monitored quantum systems and one for entanglement transitions in random tensor networks. These Lagrangians, previously…
We propose a new implementation of real-space renormalization group (RG) transformations for quantum states on a lattice. Key to this approach is the removal of short-ranged entanglement, similar to Vidal's entanglement renormalization…
Deep learning is a broad set of techniques that uses multiple layers of representation to automatically learn relevant features directly from structured data. Recently, such techniques have yielded record-breaking results on a diverse set…
We show that renormalization group (RG) theory applied to complex networks are useful to classify network topologies into universality classes in the space of configurations. The RG flow readily identifies a small-world/fractal transition…