Related papers: The Effective Average Action Beyond First Order
The recursion relations of hierarchical models are studied and contrasted with functional renormalisation group equations in corresponding approximations. The formalisms are compared quantitatively for the Ising universality class, where…
The critical behavior of the $(n+1)$-states Potts model in $d$-dimensions is studied with functional renormalization group techniques. We devise a general method to derive $\beta$-functions for continuos values of $d$ and $n$ and we write…
The derivative expansion of the effective action is a perturbative development in derivatives of the fields. The expansion breaks down when some of the derivatives are too large. We show how to sum exactly the first and second derivatives…
We apply the functional renormalization group theory to the dynamics of first-order phase transitions and show that a potential with all odd-order terms can describe spinodal decomposition phenomena. We derive a momentum-dependent dynamic…
We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A…
We compute the critical behaviour of three-dimensional scalar theories using a new exact non-perturbative evolution equation. Our values for the critical exponents agree well with previous precision estimates.
We apply the string inspired worldline formalism to the calculation of the higher derivative expansion of one-loop effective actions in non-Abelian gauge theory. For this purpose, we have completely computerized the method, using the…
By writing the flow equations for the continuum Legendre effective action (a.k.a. Helmholtz free energy) with respect to a particular form of smooth cutoff, and performing a derivative expansion up to some maximum order, a set of…
We use the large $N$ critical point formalism to compute $d$-dimensional critical exponents at several orders in $1/N$ in an Ising Gross-Neveu universality class where the core interaction includes a Lie group generator. Specifying a…
We derive an alternative to the Wetterich-Morris-Ellwanger equation by means of the two-particle irreducible (2PI) effective action, exploiting the method of external sources due to Garbrecht and Millington. The latter allows the two-point…
Recent advances in conformal field theory and critical phenomena have focused on the characterization of boundary or defects in a conformally invariant system. In this Letter we study the critical behavior of the three-dimensional Ising…
A manifestly gauge invariant continuous renormalization group flow equation is constructed for pure SU(N) gauge theory. The formulation makes sense without gauge fixing and manifestly gauge invariant calculations may thus be carried out.…
We propose a method to obtain an improved Hamiltonian (action) for the Ising universality class in three dimensions. The improved Hamiltonian has suppressed leading corrections to scaling. It is obtained by tuning models with two coupling…
We investigate the renormalization of ``nonlocal" interactions which arise as an infinite sum of higher derivative interactions in an effective field theory. Using dimensional regularization with minimal subtraction in a general scalar…
This paper derives the Feynman rules for the diagrammatic perturbation expansion of the effective action around an arbitrary solvable problem. The perturbation expansion around a Gaussian theory is well known and composed of one-line…
Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that…
For a general class of non-negative functions defined on integral ideals of number fields, upper bounds are established for their average over the values of certain principal ideals that are associated to irreducible binary forms with…
Non-perturbative exact flow equations describe the scale dependence of the effective average action. We present a numerical solution for an approximate form of the flow equation for the potential in a three-dimensional N-component scalar…
Phase transitions and critical phenomena are among the most intriguing phenomena in nature and their renormalization-group theory is one of the greatest achievements of theoretical physics. However, the predictions of the theory above an…
The renormalization group functions are calculated in $D=4-\epsilon$ dimensions for the $\phi^4$-theory with two coupling constants associated with an ${O}(N)$-symmetric and a cubic interaction. Divergences are removed by minimal…