Non-perturbative Methods in Statistical Descriptions of Turbulence

2021 ◽  
Author(s):  
Jan Friedrich
Keyword(s):  
Perturbative Methods

scholarly journals A critical look at the electroweak phase transition

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Andreas Ekstedt ◽  
Johan Löfgren
Keyword(s):  
Phase Transition ◽  
Generic Model ◽  
Electroweak Symmetry ◽  
Electroweak Phase Transition ◽  
Gauge Dependence ◽  
Perturbative Methods ◽  
The Standard Model ◽  
Gauge Fixing ◽  
Infrared Divergences ◽  
General Gauge

Abstract The electroweak phase transition broke the electroweak symmetry. Perturbative methods used to calculate observables related to this phase transition suffer from severe problems such as gauge dependence, infrared divergences, and a breakdown of perturbation theory. In this paper we develop robust perturbative tools for dealing with phase transitions. We argue that gauge and infrared problems are absent in a consistent power-counting. We calculate the finite temperature effective potential to two loops for general gauge-fixing parameters in a generic model. We demonstrate gauge invariance, and perform numerical calculations for the Standard Model in Fermi gauge.

scholarly journals TESTING PERTURBATIVE RESULTS WITH NON-PERTURBATIVE METHODS FOR THE HIERARCHICAL MODEL

2001 ◽  
Vol 16 (supp01c) ◽  
pp. 1251-1253
Author(s):  
Y. MEURICE ◽  
M. B. OKTAY
Keyword(s):  
Low Temperature ◽  
Critical Exponent ◽  
Hierarchical Model ◽  
Preliminary Results ◽  
Perturbative Methods

We present non-perturbative methods to calculate accurately the renormalized quantities for Dyson's Hierarchical Model. We apply this method and calculate the critical exponent γ with 12 and 4 significant digits in the high and low temperature phases, respectively. We report accurate values for universal ratios of amplitudes and preliminary results concerning the comparison with perturbative results.

Boundary conditions for Maxwell fields in Kerr-AdS spacetimes

2016 ◽  
Vol 25 (09) ◽  
pp. 1641011 ◽  
Author(s):  
Mengjie Wang
Keyword(s):  
Black Holes ◽  
Angular Momentum ◽  
Boundary Conditions ◽  
Energy Flux ◽  
Momentum Flux ◽  
De Sitter ◽  
Perturbative Methods ◽  
Flux Boundary Conditions ◽  
Maxwell Fields ◽  
New Type

Perturbative methods are useful to study the interaction between black holes and test fields. The equation for a perturbation itself, however, is not complete to study such a composed system if we do not assign physically relevant boundary conditions. Recently we have proposed a new type of boundary conditions for Maxwell fields in Kerr-anti-de Sitter (Kerr-AdS) spacetimes, from the viewpoint that the AdS boundary may be regarded as a perfectly reflecting mirror, in the sense that energy flux vanishes asymptotically. In this paper, we prove explicitly that a vanishing energy flux leads to a vanishing angular momentum flux. Thus, these boundary conditions may be dubbed as vanishing flux boundary conditions.

Perturbative methods: averaging

2019 ◽  
pp. 253-288
Author(s):  
H. G. Solari ◽  
M. A. Natiello ◽  
G. B. Mindlin
Keyword(s):  
Perturbative Methods

scholarly journals Symmetries of Thirring Models on 3D Lattices

2022 ◽  
Author(s):  
Andreas Wilhelm Wipf ◽  
Julian Johannes Lenz
Keyword(s):  
Phase Transition ◽  
Order Parameter ◽  
Three Dimensions ◽  
Coupling Phase ◽  
Perturbative Methods ◽  
Dirac Materials ◽  
Recent Developments ◽  
Arbitrary Dimensions ◽  
Relativistic Fermi ◽  
The Continuum

We review some recent developments about strongly interacting relativistic Fermi theories in three spacetime dimensions. These models realize the asymptotic safety scenario and are used to describe the low-energy properties of Dirac materials in condensed matter physics. We begin with a general discussion of the symmetries of multi-flavor Fermi systems in arbitrary dimensions. Then we review known results about the critical flavor number $N_\mathrm{crit}$ of Thirring models in three dimensions. Only models with flavor number below $N_\mathrm{crit}$ show a phase transition from a symmetry-broken strong-coupling phase to a symmetric weak-coupling phase. Recent simulations with chiral fermions show that $N_\mathrm{crit}$ is smaller than previously extracted with various non-perturbative methods. Our simulations with chiral SLAC fermions reveal that for four-component flavors $N_\mathrm{crit}=0.80(4)$. This means that all reducible Thirring models with $\Nr=1,2,3,\dots$ show no phase transition with order parameter. Instead we discover footprints of phase transitions without order parameter. These new transitions are probably smooth and could be used to relate the lattice Thirring models to Thirring models in the continuum. For a single irreducible flavor, we provide previously unpublished values for the critical couplings and critical exponents.

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