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We study higher derivative extension of the functional renormalization group (FRG). We consider FRG equations for a scalar field that consist of terms with higher functional derivatives of the effective action and arbitrary cutoff…

High Energy Physics - Theory · Physics 2022-07-15 Gota Tanaka , Asato Tsuchiya

We discuss how the ordinary renormalization group (RG) equations arise in the context of Wilson's exact renormalization group (ERG) as formulated by Polchinski. We consider the phi4 theory in four dimensional euclidean space as an example,…

High Energy Physics - Theory · Physics 2008-11-26 Hidenori Sonoda

The ratios $R_{2k}$ of renormalized coupling constants $g_{2k}$ that enter the effective potential and small-field equation of state acquire the universal values at criticality. They are calculated for the three-dimensional scalar…

Statistical Mechanics · Physics 2017-06-07 A. I. Sokolov , A. Kudlis , M. A. Nikitina

Using the recent six loop renormalization group functions for Lee-Yang and percolation theory constructed by Schnetz from a scalar cubic Lagrangian, we deduce the $\epsilon$ expansion of the critical exponents for both cases. Estimates for…

High Energy Physics - Theory · Physics 2025-11-03 J. A. Gracey

We employ perturbative RG and $\epsilon$-expansion to study multi-critical single-scalar field theories with higher derivative kinetic terms of the form $\phi(-\Box)^k\phi$. We focus on those with a $\mathbb{Z}_2$-symmetric critical point…

High Energy Physics - Theory · Physics 2018-02-21 Mahmoud Safari , Gian Paolo Vacca

The infrared behaviour of a non-mean field spin-glass system is analysed, and the critical exponent related to the divergence of the correlation length is computed at two loops within the epsilon-expansion technique with two independent…

Disordered Systems and Neural Networks · Physics 2014-09-12 Michele Castellana , Giorgio Parisi

We study how to compute the operator product expansion coefficients in the exact renormalization group formalism. After discussing possible strategies, we consider some examples explicitly, within the $\epsilon$-expansions, for the…

High Energy Physics - Theory · Physics 2020-05-20 C. Pagani , H. Sonoda

The determination of the critical exponents by means of the Exact Renormalizion Group approach is still a topic of debate. The general flow equation is by construction scheme independent, but the use of the truncated derivative expansion…

High Energy Physics - Theory · Physics 2011-07-19 A. Bonanno , D. Zappalà

We formulate a method of performing non-perturbative calculations in quantum field theory, based upon a derivative expansion of the exact renormalization group. We then proceed to apply this method to the calculation of critical exponents…

High Energy Physics - Theory · Physics 2007-05-23 Michael D. Turner

We give a review of the exact renormalization group (ERG) approach and illustrate its applications in scalar and fermionic theories. The derivative expansion and approximations based on the derivative expansion with further truncation in…

High Energy Physics - Theory · Physics 2008-02-03 Jordi Comellas , Yuri Kubyshin , Enrique Moreno

We study multifield extensions of Reggeon Field Theory (also equivalent to Directed Percolation model) at criticality in the perturbative epsilon-expansion below the upper critical dimension Dc=4 at one loop, for the special case when all…

High Energy Physics - Theory · Physics 2024-02-07 Jochen Bartels , Carlos Contreras , Gian Paolo Vacca

The method of self-consistent expansions is a powerful tool for handling strong coupling problems that might otherwise be beyond the reach of perturbation theory, providing surprisingly accurate approximations even at low order. First…

Statistical Mechanics · Physics 2025-01-15 Minhui Zhu , Nigel Goldenfeld

Fixed-point equations in the functional renormalization group approach are integrated from large to vanishing field, where an asymptotic potential in the limit of large field is implemented as initial conditions. This approach allows us to…

High Energy Physics - Phenomenology · Physics 2023-04-11 Yang-yang Tan , Chuang Huang , Yong-rui Chen , Wei-jie Fu

The Polchinski exact renormalization group equation for a scalar field theory in arbitrary dimensions is translated, by means of a covariant Hamiltonian formalism, into a partial differential equation for an effective Hamiltonian density…

High Energy Physics - Theory · Physics 2015-11-02 Luca Zambelli

The paper discusses extensions of the renormalization group (RG) formalism for 3D incompressible Euler equations, which can be used for describing singularities developing in finite (blowup) or infinite time from smooth initial conditions…

Fluid Dynamics · Physics 2012-05-23 Alexei A. Mailybaev

We develop a method for extracting accurate critical exponents from perturbation expansions of the O(n)-symmetric nonlinear sigma-model in D=2+ epsilon dimensions. This is possible by considering the epsilon-expansions in this model as…

High Energy Physics - Theory · Physics 2009-10-31 Hagen Kleinert

We project the Wilson/Polchinski renormalization group equation onto its uniform external field dependent effective free energy and connected Green's functions. The result is a hierarchy of equations which admits a choice of "natural"…

High Energy Physics - Theory · Physics 2007-05-23 Geoffrey R. Golner

We investigate the structure of Polchinski's formulation of the flow equations for the continuum Wilson effective action. Reinterpretations in terms of I.R. cutoff greens functions are given. A promising non-perturbative approximation…

High Energy Physics - Phenomenology · Physics 2009-10-22 Tim R. Morris

Through appropriate projections of an exact renormalization group equation, we study fixed points, critical exponents and nontrivial renormalization group flows in scalar field theories in $2<d<4$. The standard upper critical dimensions…

High Energy Physics - Theory · Physics 2009-10-22 Peter E. Haagensen , Yuri Kubyshin , Jose I. Latorre , Enrique Moreno

The establishment of the Wilson-Fisher fixed point (WFP) for $O(n)$ spin models in $d=4-\epsilon$ dimensions stands as a cornerstone of the renormalization group (RG) theory for critical phenomena. However, when long-range (LR)…

Statistical Mechanics · Physics 2026-03-20 Zhiyi Li , Kun Chen , Youjin Deng