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We present a self consistent method based on cluster algorithms and Renormalization Group on the lattice to study critical systems numerically. We illustrate it by means of the 2D Ising model. We compute the critical exponents $\nu$ and…
Identifying the relevant coarse-grained degrees of freedom in a complex physical system is a key stage in developing powerful effective theories in and out of equilibrium. The celebrated renormalization group provides a framework for this…
We explore a systematic approach to studying the dynamics of evolving networks at a coarse-grained, system level. We emphasize the importance of finding good observables (network properties) in terms of which coarse grained models can be…
Evaluation of likelihood functions for cosmological large scale structure data sets (including CMB, galaxy redshift surveys, etc.) naturally involves marginalization, i.e., integration, over an unknown underlying random signal field.…
We introduce a real time version of the functional renormalization group which allows to study correlation effects on nonequilibrium transport through quantum dots. Our method is equally capable to address (i) the relaxation out of a…
This paper studies change-points in human brain functional connectivity (FC) and seeks patterns that are common across multiple subjects under identical external stimulus. FC relates to the similarity of fMRI responses across different…
We theoretically study the electromagnetic interaction in Dirac systems with $N$ nodes by using the renormalization group, which is relevant to the quantum critical phenomena of topological phase transition ($N=1$) and Weyl semimetals…
Reentrant computation-recursive self-coupling in which a network continuously reinjects and reinterprets its own internal state-plays a central role in biological cognition but remains poorly characterized in neural network architectures.…
We study the critical behavior of the random q-state Potts quantum chain by density matrix renormalization techniques. Critical exponents are calculated by scaling analysis of finite lattice data of short chains ($L \leq 16$) averaging over…
We review current progress in the functional renormalization group treatment of disordered systems. After an elementary introduction into the phenomenology, we show why in the context of disordered systems a functional renormalization group…
The infrared behaviour of a non-mean field spin-glass system is analysed, and the critical exponent related to the divergence of the correlation length is computed at two loops within the epsilon-expansion technique with two independent…
Motivated by long-range dispersal in ecological systems, we formulate and apply a general strong-disorder renormalization group (SDRG) framework to describe one-dimensional disordered contact processes with heavy-tailed, such as power law,…
We use functional renormalization group methods to study gravity minimally coupled to a free scalar field. This setup provides the prototype of a gravitational theory which is perturbatively non-renormalizable at one-loop level, but may…
In this paper, we introduce new reference observables to establish a scaling formula in the renormalization group equation. Using the transfer matrix method, we calculate the two point observables of the one dimensional Ising model without…
We apply the non-perturbative renormalization group method to a class of out-of-equilibrium phase transitions (usually called ``parity conserving'' or, more properly, ``generalized voter'' class) which is out of the reach of perturbative…
The experimental study of neural networks requires simultaneous measurements of a massive number of neurons, while monitoring properties of the connectivity, synaptic strengths and delays. Current technological barriers make such a mission…
We derive a new renormalization group to calculate a non-trivial critical exponent of the divergent correlation length which gives a universality classification of essential singularities in infinite-order phase transitions. This method…
The random-field Ising model shows extreme critical slowdown that has been described by activated dynamic scaling: the characteristic time for the relaxation to equilibrium diverges exponentially with the correlation length, $\ln \tau\sim…
A renormalization group transformation suitable for spin glass models and, more generally, for disordered models, is presented. The procedure is non-standard in both the nature of the additional interactions and the coarse graining…
A relation between geometric phases and criticality of spin chains are studied by using the quantum renormalization-group approach. We have shown how the geometric phase evolve as the size of the system becomes large, i.e., the finite size…