Quantum critical scenario from an effective classical renormalization group treatment close to and below four dimensions

2005 ◽  
Vol 344 (6) ◽  
pp. 395-400 ◽  
Author(s):  
M.T. Mercaldo ◽  
I. Rabuffo ◽  
A. Caramico D'Auria ◽  
L. De Cesare
Keyword(s):  
Renormalization Group ◽  
Group Treatment ◽  
Four Dimensions ◽  
Quantum Critical

Real-space renormalization-group treatment of the Maier-Saupe-Zwanzig model for biaxial nematic structures

2021 ◽  
Vol 103 (3) ◽  
Author(s):  
Cícero T. G. dos Santos ◽  
André P. Vieira ◽  
Silvio R. Salinas ◽  
Roberto F. S. Andrade
Keyword(s):  
Renormalization Group ◽  
Group Treatment ◽  
Real Space ◽  
Real Space Renormalization Group ◽  
Biaxial Nematic

Generalized renormalization group treatment of the growth kinetics of unstable systems

1985 ◽  
Vol 41 (1-2) ◽  
pp. 17-36 ◽  
Author(s):  
Scott R. Anderson ◽  
Gene F. Mazenko ◽  
Oriol T. Valls
Keyword(s):  
Renormalization Group ◽  
Growth Kinetics ◽  
Group Treatment ◽  
Unstable Systems ◽  
Kinetics Of

Infrared Yang–Mills theory: A renormalization group perspective

2016 ◽  
Vol 25 (07) ◽  
pp. 1642002 ◽  
Author(s):  
Axel Weber ◽  
Pietro Dall’Olio ◽  
Francisco Astorga
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Analytical Approach ◽  
Landau Gauge ◽  
Momentum Dependence ◽  
Lattice Data ◽  
Four Dimensions ◽  
Yang Mills ◽  
Epsilon Expansion ◽  
Renormalization Group Equations

We describe a technically very simple analytical approach to the deep infrared regime of Yang–Mills theory in the Landau gauge via Callan–Symanzik renormalization group equations in an epsilon expansion. This approach recovers all the solutions for the infrared gluon and ghost propagators previously found by solving the Dyson–Schwinger equations of the theory and singles out the solution with decoupling behavior, confirmed by lattice calculations, as the only one corresponding to an infrared attractive fixed point (for space-time dimensions above two). For the case of four dimensions, we describe the crossover of the system from the ultraviolet to the infrared fixed point and determine the complete momentum dependence of the propagators. The results for different renormalization schemes are compared to the lattice data.

scholarly journals Isotropic Lifshitz scaling in four dimensions

2020 ◽  
Vol 17 (04) ◽  
pp. 2050053 ◽  
Author(s):  
Dario Zappalà
Keyword(s):  
Renormalization Group ◽  
Fixed Points ◽  
Critical Dimension ◽  
Two Dimensional ◽  
Continuous Line ◽  
Scalar Theory ◽  
Functional Renormalization Group ◽  
Four Dimensions ◽  
Dimension Formula

The presence of isotropic Lifshitz points for a [Formula: see text]-symmetric scalar theory is investigated with the help of the Functional Renormalization Group. In particular, at the supposed lower critical dimension [Formula: see text], evidence for a continuous line of fixed points is found for the [Formula: see text] theory, and the observed structure presents clear similarities with the properties observed in the two-dimensional Berezinskii–Kosterlitz–Thouless phase.

scholarly journals Six-dimensional ultraviolet completion of the ℂℙ(N) σ model at two loops

2020 ◽  
Vol 35 (22) ◽  
pp. 2050188
Author(s):  
J. A. Gracey
Keyword(s):  
Renormalization Group ◽  
Quantum Electrodynamics ◽  
Matter Field ◽  
Coupling Constants ◽  
Universal Theory ◽  
Gauge Parameter ◽  
Loop Analysis ◽  
Four Dimensions ◽  
Anomalous Dimensions ◽  
Group Functions

We extend the recent one-loop analysis of the ultraviolet completion of the [Formula: see text] nonlinear [Formula: see text] model in six dimensions to two-loop order in the [Formula: see text] scheme for an arbitrary covariant gauge. In particular we compute the anomalous dimensions of the fields and [Formula: see text]-functions of the four coupling constants. We note that like Quantum Electrodynamics (QED) in four dimensions the matter field anomalous dimension only depends on the gauge parameter at one loop. As a nontrivial check we verify that the critical exponents derived from these renormalization group functions at the Wilson–Fisher fixed point are consistent with the [Formula: see text] expansion of the respective large [Formula: see text] exponents of the underlying universal theory. Using the Ward–Takahashi identity we deduce the three-loop [Formula: see text] renormalization group functions for the six-dimensional ultraviolet completeness of scalar QED.

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