Related papers: New universality classes for generic higher charac…
The study of critical properties of systems with long-range interactions has attracted in the last decades a continuing interest and motivated the development of several analytical and numerical techniques, in particular in connection with…
A classification of critical behavior is provided in systems for which the renormalization group equations are control-parameter dependent. It describes phase transitions in networks with a recursive, hierarchical structure but appears to…
The planar Heisenberg system with antiferroquadrupolar exchange on 3D stacked triangular lattice is shown to belong to the new "chiral" universality class, predicted for chiral antiferromagnets. The present system, however, displays no such…
We develop the concept of character level for the complex irreducible characters of finite, general or special, linear and unitary groups. We give characterizations of the level of a character in terms of its Lusztig's label and in terms of…
We derive exact renormalization-group recursion relations for an Ising model, in the presence of external fields, with ferromagnetic nearest-neighbor interactions on Migdal-Kadanoff hierarchical lattices. We consider layered distributions…
We propose a new line of attack to create a finite quantum theory which includes general relativity and (perhaps) the standard model in its low energy limit. The theory would emerge from the categorical approach. A structure is observed on…
Motivated by some recent criticisms to our alternative Langevin equation for driven lattice gases (DLG) under an infinitely large driving field, we revisit the derivation of such an equation, and test its validity. As a result, an…
We study a self-organized critical system under influence of turbulent motion of the environment. The system is described by the anisotropic continuous stochastic equation proposed by Hwa and Kardar [{\it Phys. Rev. Lett.} {\bf 62}: 1813…
We discuss universality in random matrix theory and in the study of Hamiltonian partial differential equations. We focus on universality of critical behavior and we compare results in unitary random matrix ensembles with their counterparts…
Interacting physical systems in the neighborhood of criticality (and massive continuum field theories) can often be characterized by just two physical scales: a (macroscopic) correlation length and a (microscopic) interaction range, related…
We study unitarity and renormalizability in the Lifshitz scalar field theory, which is characterized by an anisotropic scaling between the space and time directions. Without the Lorentz symmetry, both the unitarity and the renormalizability…
We continue the development of the theory of infinitesimal Lipschitz equivalence, showing the genericity of the condition for families of hypersurfaces with isolated singularities.
The problem of adversarial examples has highlighted the need for a theory of regularisation that is general enough to apply to exotic function classes, such as universal approximators. In response, we give a very general equality result…
We analyze critical points that can be induced in glassy systems by the presence of constraints. These critical points are predicted by the Mean Field Thermodynamic approach and they are precursors of the standard glass transition in…
This paper introduces new parameterizations of equilibrium neural networks, i.e. networks defined by implicit equations. This model class includes standard multilayer and residual networks as special cases. The new parameterization admits a…
Critical behaviour of a fluid, subjected to strongly anisotropic turbulent mixing, is studied by means of the field theoretic renormalization group. As a simplified model, relaxational stochastic dynamics of a non-conserved scalar order…
An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential…
It is shown that intrinsically anisotropic non-equilibrium systems relaxing by a dynamic process exhibit universal critical behavior during their evolution toward non-equilibrium stationary states. An anisotropic scaling anzats for the…
We show that one-dimensional quantum systems with gapless degrees of freedom and open boundary conditions form a new universality class of quantum critical behavior, which we propose to call ``bounded Luttinger liquids''. They share the…
These lecture notes have been written for a short introductory course on universality and renormalization group techniques given at the VIII Modave School in Mathematical Physics by the author, intended for PhD students and researchers new…