An Introduction to the Nonperturbative Renormalization Group

Abstract

An elementary introduction to the non-perturbative renormalization group is presented mainly in the context of statistical mechanics. No prior knowledge of field theory is necessary. The aim is this article is not to give an extensive overview of the subject but rather to insist on conceptual aspects and to explain in detail the main technical steps. It should be taken as an introduction to more advanced readings.

56 pages

References in corpus (6)

• Exact evolution equation for the effective potential
• Flow Equations for the BCS-BEC Crossover
• Non-perturbative fixed point in a non-equilibrium phase transition
• Non perturbative renormalisation group and momentum dependence of $n$-point functions (I)
• Non perturbative renormalization group and momentum dependence of n-point functions (II)
• Non-Perturbative Renormalization Group for Simple Fluids

Cited by in corpus (222)

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• On the Functional Renormalization Group approach for Yang-Mills fields
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• Multicritical behavior in models with two competing order parameters
• Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition
• Criticality of Spin Systems with Weak Long-Range Interactions
• Essential Quantum Einstein Gravity
• Renormalizable Group Field Theory beyond melonic diagrams: an example in rank four
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• An asymptotic safety scenario for gauged chiral Higgs-Yukawa models
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• Mobile impurity in a Fermi sea from the functional renormalization group analytically continued to real time
• Universal location of Yang-Lee edge singularity for a one-component field theory in $1\le d\le 4$
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• KPZ equation with short-range correlated noise: emergent symmetries and non-universal observables
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• Scheme dependence of asymptotically free solutions
• Functional renormalization group for multilinear disordered Langevin dynamics I: Formalism and first numerical investigations at equilibrium
• Topological phase transitions in four dimensions
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• Critical phenomena at the complex tensor ordering phase transition
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• Superuniversal transport near a $(2+1)$-dimensional quantum critical point
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• Existence and Construction of Exact FRG Flows of a UV-Interacting Scalar Field Theory
• Is there a Mott-glass phase in a one-dimensional disordered quantum fluid with linearly confining interactions?
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• Renormalization Group Flow of the Higgs Potential
• Nontrivial UV behavior of rank-4 tensor field models for quantum gravity
• The two upper critical dimensions of the Ising and Potts models
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• The inviscid fixed point of the multi-dimensional Burgers-KPZ equation
• Simulating frustrated magnetism with spinor Bose gases
• Effective scalar potential in asymptotically safe quantum gravity
• First-order phase transitions in spinor Bose gases and frustrated magnets
• Renormalization group flow equations with full momentum dependence
• No Ward-Takahashi identity violation for an Abelian tensorial group field theories with closure constraint
• Dimensional crossover in ultracold Fermi gases from Functional Renormalisation
• Vainshtein in the UV and a Wilsonian analysis of derivatively coupled scalars
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• Exploring the different phase diagrams of Strong Interactions
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• Nonperturbative Renormalization Group for the Landau-de Gennes Model
• On the maximal noise for stochastic and QCD traveling waves
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• On the effective action in presence of local non-linear constraints
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• Unified Functional-Holographic Theory of the QCD Critical End Point
• Functional Renormalization Group Approach for Signal Detection
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• Momentum-dependence in the infinitesimal Wilsonian renormalization group
• An asymptotic-safety mechanism for chiral Yukawa systems
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• Critical and multicritical Lee-Yang fixed points in the local potential approximation
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• Renormalization group approach to the elastic properties of graphene bilayers
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