Related papers: Global Wilson-Fisher fixed points
We investigate the $O(N)$--symmetric $\phi^6$ theory in three spacetime dimensions using dimensional regularisation and minimal subtraction. The predictions of other methods are scrutinised in a large-$N$ expansion. We show how the…
We construct novel conformal sigma models in three dimensions. Nonlinear sigma models in three dimensions are nonrenormalizable in perturbation theory. We use Wilsonian renormalization group equation method to find the fixed points.…
We explore universal critical behavior in models with two competing order parameters, and an O(N)+O(M) symmetry for dimensions $d \leq 3$. In d=3, there is always exactly one stable Renormalization Group fixed point, corresponding to…
The effect of the $\ord{\partial^4}$ terms of the gradient expansion on anomalous dimension $\eta$ and the correlation length's critical exponent $\nu$ of the Wilson-Fisher fixed point has been determined for the Euclidean $O(N)$ model for…
We renormalize the six dimensional cubic theory with an $O(N)$ $\times$ $O(m)$ symmetry at three loops in the modified minimal subtraction (MSbar) scheme. The theory lies in the same universality class as the four dimensional…
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…
We propose a novel scheme for the exact renormalisation group motivated by the desire of reducing the complexity of practical computations. The key idea is to specify renormalisation conditions for all inessential couplings, leaving us with…
Non-Fermi liquids in $d>2$ remain poorly understood, particularly when relevant perturbations destabilize them. In one spatial dimension, chirally stabilized fixed points provide a rare class of analytically tractable non-Fermi-liquid…
We derive a supersymmetric renormalization group (RG) equation for the scale-dependent superpotential of the supersymmetric O(N) model in three dimensions. For a supersymmetric optimized regulator function we solve the RG equation for the…
It is argued that universality is severely limited for models with multiple fixed points. As a demonstration the renormalization group equations are presented for the potential and the wave function renormalization constants in the $O(N)$…
We investigate finite lattice approximations to the Wilson Renormalization Group in models of unconstrained spins. We discuss first the properties of the Renormalization Group Transformation (RGT) that control the accuracy of this type of…
We study the Principal Chiral Ginzburg-Landau-Wilson model around two dimensions within the Local Potential Approximation of an Exact Renormalization Group equation. This model, relevant for the long distance physics of classical frustrated…
Wilson's original formulation of the renormalization group is perturbative in nature. We here present an alternative derivation of the infinitesimal momentum shell RG, akin to the Wegner and Houghton scheme, that is a priori exact. We show…
The functional flow equations for the Legendre effective action, with respect to changes in a smooth cutoff, are approximated by a derivative expansion; no other approximation is made. This results in a set of coupled non-linear…
We determine a previously unknown universal quantity, the location of the Yang-Lee edge singularity for the O($N$) theories in a wide range of $N$ and various dimensions. At large $N$, we reproduce the $N\to\infty$ analytical result on the…
Using an Environmentally Friendly Renormalization Group we derive an ab initio universal scaling form for the equation of state for the O(N) model, y=f(x), that exhibits all required analyticity properties in the limits $x\to 0$,…
We write new functional renormalization group equations for a scalar nonminimally coupled to gravity. Thanks to the choice of the parametrization and of the gauge fixing they are simpler than older equations and avoid some of the…
Renormalization group methods are used to determine the evolution of the low energy Wilson effective action for supersymmetric nonlinear sigma models in four dimensions. For the case of supersymmetric $CP^{(N-1)}$ models, the K\"ahler…
We give a rigorous nonperturbative construction of a massless discrete trajectory for Wilson's exact renormalization group. The model is a three dimensional Euclidean field theory with a modified free propagator. The trajectory realizes the…
In this work we re-examine the Wilson Fisher fixed point. We study Wilsonian momentum space renormalization group (RG) flow for various forms of the cutoff. We show that already at order $\left(4-d\right)^{1}$, where $d$ is the dimension of…