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This paper presents the foundational ideas for a new way of modeling social aggregation. Traditional approaches have been using network theory, and the theory of random networks. Under that paradigm, every social agent is represented by a…
Synchronization processes play critical roles in the functionality of a wide range of both natural and man-made systems. Recent work in physics and neuroscience highlights the importance of higher-order interactions between dynamical units,…
Complex networks represent the natural backbone to study epidemic processes in populations of interacting individuals. Such a modeling framework, however, is naturally limited to pairwise interactions, making it less suitable to properly…
Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of nonlinear systems. There have been recent efforts to generalize SRG analysis to Multiple-Input Multiple-Output (MIMO) systems. However,…
Capturing the interplay between electronic correlations and many-particle entanglement requires a unified framework for Hamiltonian and eigenbasis renormalization. In this work, we apply the unitary renormalization group (URG) scheme…
We show that the Tensor Renormalization Group (TRG) method can be applied to O(N) spin models, principal chiral models and pure gauge theories (Z2, U(1) and SU(2)) on (hyper) cubic lattices. We explain that contrarily to some common belief,…
The Renormalisation Group (RG) is a systematic procedure used to regularise divergences appearing as artefacts when constructing solutions to a large class of differential problems, whether perturbatively or not. This paper is devoted to…
The "critical brain hypothesis" posits that neural circuitry may be tuned close to a "critical point" or "phase transition" -- a boundary between different operating regimes of the circuit. The renormalization group and theory of critical…
We study the surface critical behavior of semi-infinite systems belonging to the bulk universality class of the Ising model. Special attention is paid to the local behavior of experimentally relevant quantities such as the order parameter…
Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a…
Real-world optimization problems may have a different underlying structure. In black-box optimization, the dependencies between decision variables remain unknown. However, some techniques can discover such interactions accurately. In Large…
By choosing appropriate generators for the Similarity Renormalization Group (SRG) flow equations, different patterns of decoupling in a Hamiltonian can be achieved. Sharp and smooth block-diagonal forms of phase-shift equivalent…
We clarify the notion of Wilsonian renormalization group (RG) invariance in supersymmetric gauge theories, which states that the low-energy physics can be kept fixed when one changes the ultraviolet cutoff, provided appropriate changes are…
Phase transitions of the $J_1$-$J_2$ Ising model on a square lattice are studied using the higher-order tensor renormalization group(HOTRG) method. This system involves a competition between the ferromagnetic interaction $J_1$ and…
Renormalisation group (RG) methods provide one of the most important techniques for analysing the physics of many-body systems, both analytically and numerically. By iterating an RG map, which "course-grains" the description of a many-body…
Presented in this thesis are a set of projects which lie at the intersection between strong correlations and topological phases of matter. The first of these projects is a treatment of an infinite dimensional generalization of the SSH model…
The tensor-network renormalization group (TNRG) is an accurate numerical real-space renormalization group method for studying phase transitions in both quantum and classical systems. Continuous phase transitions, as an important class of…
Molecular interactions often involve high-order relationships that cannot be fully captured by traditional graph-based models limited to pairwise connections. Hypergraphs naturally extend graphs by enabling multi-way interactions, making…
Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…
We develop a multiscale approach to estimate high-dimensional probability distributions from a dataset of physical fields or configurations observed in experiments or simulations. In this way we can estimate energy functions (or…