Related papers: New Fixed Points from Melonic Interactions
We consider the zero-temperature fixed points controlling the critical behavior of the $d$-dimensional random-field Ising, and more generally $O(N)$, models. We clarify the nature of these fixed points and their stability in the region of…
The all-orders beta function is used to study disordered Dirac fermions in 2D. The generic strong coupling fixed `points' of anisotropic current-current interactions at large distances are actually isotropic manifolds corresponding to…
Several results related to flat Friedmann-Lema\^{\i}tre-Robertson-Walker models in the conformal (Einstein) frame of scalar-tensor gravity theories are extended. Scalar fields with arbitrary (positive) potentials and arbitrary coupling…
It has long been known that particles with short-range repulsive interactions in spatial dimension d=1 form universal quantum liquids in the low density limit: all properties can be related to those of the spinless free Fermi gas. Previous…
Many models of flocking involve alignment rules based on the mean orientation of neighboring particles, which we show introduces microscopic non-reciprocal interactions. In the absence of this microscopic non-reciprocity an exceptional…
The dynamics at the IR fixed point realized in the $SU(N_c)$ gauge theories with massless Dirac fermions is studied by means of the non-perturbative renormalization group. The analysis includes the IR fixed points with non-trivial Yukawa…
Using an elementary argument, we prove new fixed point theorems for classical elliptic complexes. We obtain new results for conformal relations and coisotropic intersections. We obtain theorems for the average intersections of families of…
Tensor models provide a way to access the path-integral for discretized quantum gravity in d dimensions. As in the case of matrix models for two-dimensional quantum gravity, the continuum limit can be related to a Renormalization Group…
Using the renormalization group approach, the Coulomb gas and the coset techniques, the effect of slightly relevant perturbations is studied for the second parafermionic field theory with the symmetry $Z_{N}$, for N odd. New fixed points…
As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces:…
The stability of nonrelativistic fermionic systems to interactions is studied within the Renormalization Group framework. A brief introduction to $\phi^4$ theory in four dimensions and the path integral formulation for fermions is given.…
Old folklore says that there is no non-trivial renormalization group fixed point with $U(1)$ gauge symmetry in four dimensions, but it can be circumvented by the existence of magnetic monopoles. We propose to construct (potentially…
A Self Consistent Field Theory description of equilibrium, but non uniform, configurations adopted by semi flexible liquid crystal molecules is presented. Two cases are considered, isotropic-nematic phase boundaries, and topological defects…
For some theories where the degrees of freedom are tensors of rank $3$ or higher, there exist solvable large $N$ limits dominated by the melonic diagrams. Simple examples are provided by models containing one rank-$3$ tensor in the…
Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and the asymptotic…
In the tensor network approach to statistical physics, properties of the critical point of a 2D lattice model are encoded by a four-legged tensor which is a fixed point of an RG map. The traditional way to find the fixed point tensor…
The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…
A hybrid of the critical three dimensional Gross-Neveu and Thirring models deformed by explicit parity breaking operators is studied in the large N expansion and using the renormalization group. The regime of coupling constants where the…
We study the UV behaviour of actions including integer powers of scalar curvature and even powers of scalar fields with Functional Renormalization Group techniques. We find UV fixed points where the gravitational couplings have non-trivial…
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…