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We summarize our recent results on the large N renormalization group (RG) approach to matrix models for discretized two-dimensional quantum gravity. We derive exact RG equations by solving the reparametrization identities, which reduce…
The renormalization group (RG) in statistical physics focuses on ground-state properties of equilibrium systems. However, it is unclear how it should be generalized to nonunitary quantum dynamics caused by dissipation and measurement…
High resolution Neutron Spin Echo (NSE) spectroscopy was used to investigate the dynamics of an 3D Heisenberg ferromagnet in the exchange-controlled regime over a broad range of temperatures and momentum transfer. These results allow for…
We analyze the statistical mechanics of a free-standing quantum crystalline membrane within the framework of a systematic perturbative renormalization group (RG). A power-counting analysis shows that the leading singularities of correlation…
We derive a general formula for the RG improved effective (Coleman-Weinberg) potential for classically conformal models, applying it to several examples of physical interest, and in particular a model of QCD coupled via quarks to a…
Spin-glasses are natural Gibbs distributions that have been studied in Theoretical CS for many decades. Recently, they have been gaining attention from the community as they emerge naturally in neural computation and learning, network…
We propose new approach for treatment of local and non-local interactions in correlated electronic systems, which uses self-energy and the two-particle irreducible vertices, obtained from (extended) dynamical mean-field theory, as an input…
Following an approach of Matarrese and Pietroni, we derive the functional renormalization group (RG) flow of the effective action of cosmological large-scale structures. Perturbative solutions of this RG flow equation are shown to be…
The renormalization group (RG) is used to study the asymptotically free $\phi_6^3$-theory in curved spacetime. Several forms of the RG equations for the effective potential are formulated. By solving these equations we obtain the one-loop…
In the framework of dimensional regularization, we propose a generalization of the renormalization group equations in the case of the perturbative quantum gravity that involves renormalization of the metric and of the higher order Riemann…
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…
We reconsider critical properties of O(N) scalar models with cubic interactions in $d>4$ dimensions using functional renormalization group equations. Working at next-to-leading order in the derivative expansion, we find non-trivial IR fixed…
We extend the exact multilocal renormalization group (RG) method to study the flow of the effective action functional. This important physical quantity satisfies an exact RG equation which is then expanded in multilocal components.…
We apply the functional Renormalisation Group (fRG) to study relaxation in a stochastic process governed by an overdamped Langevin equation with one degree of freedom, exploiting the connection with supersymmetric quantum mechanics in…
The renormalization group is used to sum the leading-log (LL) contributions to the effective action for a large constant external gauge field in terms of the one-loop renormalization group (RG) function beta, the next-to-leading-log (NLL)…
We suggest to consider conformal factor dynamics as applying to composite boundstates, in frames of the $1/N$ expansion. In this way, a new model of effective theory for quantum gravity is obtained. The renormalization group (RG) analysis…
We apply field theoretical renormalization group (RG) methods to describe the Tomonaga-Luttinger model as an important test ground to deal with spin-charge separation effects in higher spatial dimensions. We compute the anomalous dimension…
The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for…
We develop a renormalization group (RG)-based perturbation scheme for a class of ordinary differential equations, including first-order systems with semisimple or nilpotent linear parts, as well as scalar higher-order equations. The key…
In this paper, we study the equilibrium states of a $N\times N$ stochastic complex random matrix $M$, whose entries evolve in time accordingly with a Langevin equation including both Gaussian white noises and a linear disorder, materialized…