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Various aspects of the Exact Renormalization Group (ERG) are explored, starting with a review of the concepts underpinning the framework and the circumstances under which it is expected to be useful. A particular emphasis is placed on the…

First-order phase transitions in many-fermion systems are not detected in the susceptibility analysis of common renormalization-group (RG) approaches. Here we introduce a counterterm technique within the functional renormalization-group…

The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our…

We systematically investigate theoretical uncertainties in perturbative analyses of first-order electroweak phase transitions (EWPT). Utilizing the Standard Model Effective Field Theory (SMEFT) framework, we quantify the gauge dependence,…

The renormalization group method has been adapted to the analysis of the long-time behavior of non-linear partial differential equation and has demonstrated its power in the study of critical phenomena of gravitational collapse. In the…

We propose the study of the phase transition in the scalar electroweak theory at finite temperature by a two - step method. It combines i) dimensional reduction to a 3-dimensional {\it lattice\/} theory via perturbative blockspin…

We briefly discuss five topics in Precision Electroweak Physics: i) the recently proposed Effective Scheme of Renormalization, ii) evidence for electroweak bosonic corrections derived from the radiative correction Delta_r_eff, iii) an…

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…

I review the progress made in recent years with functional methods in our understanding of the QCD phase diagram. In particular I discuss a renormalisation group approach to QCD at finite temperature and chemical potential. Results include…

We investigate the thermodynamic geometry of the quark-meson model at finite temperature, $T$, and quark number chemical potential, $\mu$. We extend previous works by the inclusion of fluctuations exploiting the functional renormalization…

The renormalization group is applied to the phi4 model in the symmetry broken phase in order to identify different scaling regimes. The new scaling laws reflect nonuniversal behavior at the phase transition. The extension of the analysis to…

A quantitative discussion of nonperturbative effects for the high temperature electroweak phase transition is presented. We propose a method for the computation of the temperature dependent effective scalar potential that takes into account…

The renormalization group method is a successive integration over the fluctuations which are ordered according to their length scale, a parameter in the external space. A different procedure is described, where the fluctuations are treated…

Modification of the renormalization-group approach, invoking Stratonovich transformation at each step, is proposed to describe phase transitions in 3D Ising-class systems. The proposed method is closely related to the mean-field…

We discuss motivation and goals of renormalization analyses of group field theory models of simplicial 4d quantum gravity, and review briefly the status of this research area. We present some new computations of perturbative GFT (spin foam)…

We unveil the temperature-dependent electroweak phase transition in new extensions of the Standard Model in which the electroweak symmetry is spontaneously broken via strongly coupled, nearly-conformal dynamics achieved by the means of…

It is well known that the electroweak phase transition (EWPhT) in extensions of the Standard Model with one real scalar singlet can be first-order for realistic values of the Higgs mass. We revisit this scenario with the most general…

We work out a set of simple rules for adopting the two-loop renormalization group equations of a generic gauge field theory given in the seminal works of Machacek and Vaughn to the most general case with an arbitrary number of Abelian gauge…

Renormalization group methods are used to study the low-energy behavior of the unscreened Coulomb interaction in a one-dimensional electron system. By applying a GW approximation, a strong wavefunction renormalization is found in the model,…

The advantages of using more than one renormalization group (RG) in problems with more than one important length scale are discussed. It is shown that: i) using different RG's can lead to complementary information, i.e. what is very…