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Recent years witnessed an extensive development of the theory of the critical point in two-dimensional statistical systems, which allowed to prove {\it existence} and {\it conformal invariance} of the {\it scaling limit} for two-dimensional…
Power-law scaling in coarse-grained data suggests critical dynamics, but the true source of this scaling often remains unclear. Here, we analyze neural activity recorded during spatial navigation, reproducing power-law scaling under a…
We review recent developments in tensor network approaches, focusing on renormalization group methods. Since they are free from the negative sign and complex action problems, there is growing interest in their application to lattice field…
We study critical and universal behaviors of unitary invariant non-gaussian random matrix ensembles within the framework of the large-N renormalization group. For a simple double-well model we find an unstable fixed point and a stable…
We investigate the role of clustering on the critical behavior of the contact process (CP) on small-world networks using the Watts-Strogatz (WS) network model with an edge rewiring probability p. The critical point is well predicted by a…
Discrete amorphous materials are best described in terms of arbitrary networks which can be embedded in three dimensional space. Investigating the thermodynamic equilibrium as well as non-equilibrium behavior of such materials around second…
Applying functional renormalization group methods, we describe two inequivalent ways of defining the renormalization group of matter-coupled four dimensional gravity, in the approximation where only the conformal factor is dynamical and…
The quantum critical behavior and the Griffiths-McCoy singularities of random quantum Ising ferromagnets are studied by applying a numerical implementation of the Ma-Dasgupta-Hu renormalization group scheme. We check the procedure for the…
Layers of two-dimensional materials arranged at a twist angle with respect to each other lead to enlarged unit cells with potentially strongly altered band structures, offering a new arena for novel and engineered many-body ground states.…
The transverse-field Ising models with random exchange interactions in finite dimensions are investigated by means of a real-space renormalization-group method. The scheme yields the exact values of the critical point and critical exponent…
Synaptic plasticity and neuron cross-talk are some of the important key mechanisms underlying formation of dynamic clusters of active neurons. The essence of this study is to model and decipher the mechanism of emergence of a task-specific…
We have developed a nonperturbative functional renormalization group approach for random field models and related disordered systems for which, due to the existence of many metastable states, conventional perturbation theory often fails.…
In this thesis, we perform a comprehensive renormalization group analysis of two- and three-dimensional Fermi systems at low and zero temperature. We examine systems with spontaneous symmetry-breaking and quantum critical behavior by…
Recent experimental observations have supported the hypothesis that the cerebral cortex operates in a dynamical regime near criticality, where the neuronal network exhibits a mixture of ordered and disordered patterns. However, A…
We report on the nature of the thermal denaturation transition of homogeneous DNA as determined from a renormalisation group analysis of the Peyrard-Bishop-Dauxois model. Our approach is based on an analogy with the phenomenon of critical…
We develop a renormalization group method to investigate synchronization clusters in a one-dimensional chain of nearest-neighbor coupled phase oscillators. The method is best suited for chains with strong disorder in the intrinsic…
Recent experimental results based on multi-electrode and imaging techniques have reinvigorated the idea that large neural networks operate near a critical point, between order and disorder. However, evidence for criticality has relied on…
The renormalization group is not only a powerful method for describing universal properties of phase transitions but it is also useful for evaluating non- universal properties beyond mean-field theory. In this contribution we concentrate on…
A field-theoretic description of the critical behavior of weakly disordered systems with a $p$-component order parameter is given. For systems of an arbitrary dimension in the range from three to four, a renormalization group analysis of…
The renormalization group has played an important role in the physics of the second half of the twentieth century both as a conceptual and a calculational tool. In particular it provided the key ideas for the construction of a qualitative…