scholarly journals Three-loop renormalization-group analysis of a complex model with stable fixed point: Critical exponents up toε3andε4

1998 ◽  
Vol 57 (6) ◽  
pp. 3562-3576 ◽  
Author(s):  
A. I. Mudrov ◽  
K. B. Varnashev
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Critical Exponents ◽  
Group Analysis ◽  
Complex Model ◽  
Stable Fixed Point ◽  
Renormalization Group Analysis

Critical Exponents for the Model with Unique Stable Fixed Point From Three-Loop RG Expansions

1998 ◽  
Vol 12 (12n13) ◽  
pp. 1365-1377 ◽  
Author(s):  
A. I. Sokolov ◽  
K. B. Varnashev ◽  
A. I. Mudrov
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Critical Exponents ◽  
Structural Transition ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Flow Diagram ◽  
Stable Fixed Point ◽  
Loop Order ◽  
Symmetry Properties

The critical behavior of a model describing phase transitions in cubic and tetragonal anti-ferromagnets with 2N-component (N>1) real order parameters as well as the structural transition in NbO 2 crystal is studied within the field-theoretical renormalization-group (RG) approach in three and (4-∊)-dimensions. Perturbative expansions for RG functions are calculated up to three-loop order and resummed, in 3D, by means of the generalized Padé–Borel procedure which is shown to preserve the specific symmetry properties of the model. It is found that a stable fixed point does exist in the three-dimensional RG flow diagram for N>1, in accordance with predictions obtained earlier within the ∊-expansion. Fixed-point coordinates and critical-exponent values are presented for physically interesting cases N=2 and N=3. In both cases critical exponents are found to be numerically close to those of the 3DXY model. The analysis of the results given by the ∊-expansion and by the RG approach in three dimensions is performed resulting in a conclusion that the latter provides much more accurate numerical estimates.

scholarly journals Dark Side of Weyl Gravity

Universe ◽  
2020 ◽  
Vol 6 (8) ◽  
pp. 123
Author(s):  
Petr Jizba ◽  
Lesław Rachwał ◽  
Stefano G. Giaccari ◽  
Jaroslav Kňap
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Cosmological Constant ◽  
Group Analysis ◽  
Dark Side ◽  
Renormalization Group Analysis ◽  
Intermediate Energies ◽  
Weyl Gravity ◽  
Trace Anomaly ◽  
Non Gaussian

We address the issue of a dynamical breakdown of scale invariance in quantum Weyl gravity together with related cosmological implications. In the first part, we build on our previous work [Phys. Rev. D2020, 101, 044050], where we found a non-trivial renormalization group fixed point in the infrared sector of quantum Weyl gravity. Here, we prove that the ensuing non-Gaussian IR fixed point is renormalization scheme independent. This confirms the feasibility of the analog of asymptotic safety scenario for quantum Weyl gravity in the IR. Some features, including non-analyticity and a lack of autonomy, of the system of β-functions near a turning point of the renormalization group at intermediate energies are also described. We further discuss an extension of the renormalization group analysis to the two-loop level. In particular, we show universal properties of the system of β-functions related to three couplings associated with C2 (Weyl square), G (Gauss–Bonnet), and R2 (Ricci curvature square) terms. Finally, we discuss various technical and conceptual issues associated with the conformal (trace) anomaly and propose possible remedies. In the second part, we analyze physics in the broken phase. In particular, we show that, in the low-energy sector of the broken phase, the theory looks like Starobinsky f(R) gravity with a gravi-cosmological constant that has a negative sign in comparison to the usual matter-induced cosmological constant. We discuss implications for cosmic inflation and highlight a non-trivial relation between Starobinsky’s parameter and the gravi-cosmological constant. Salient issues, including possible UV completions of quantum Weyl gravity and the role of the trace anomaly matching, are also discussed.

scholarly journals INTERPLAY OF FIXED POINTS IN SCALAR MODELS

2013 ◽  
Vol 28 (26) ◽  
pp. 1350130 ◽  
Author(s):  
S. NAGY ◽  
K. SAILER
Keyword(s):  
Phase Transition ◽  
Fixed Point ◽  
Renormalization Group ◽  
Symmetry Breaking ◽  
Critical Exponent ◽  
Correlation Length ◽  
Group Analysis ◽  
Renormalization Group Analysis ◽  
The One ◽  
Symmetric Phase

We performed the renormalization group analysis of scalar models exhibiting spontaneous symmetry breaking. It is shown that an infrared fixed point appears in the broken symmetric phase of the models, which induces a dynamical scale, that can be identified with the correlation length. This enables one to identify the type of the phase transition which shows similarity to the one appearing in the crossover scale. The critical exponent ν of the correlation length also proved to be equal in the crossover and the infrared scaling regimes.

scholarly journals ONE-LOOP RENORMALIZATION GROUP ANALYSIS OF BOSE–FERMI MIXTURES

2012 ◽  
Vol 26 (32) ◽  
pp. 1250197
Author(s):  
BOYANG LIU ◽  
JIANGPING HU
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Group Analysis ◽  
Three Dimensional ◽  
Coupling Constants ◽  
Tree Level ◽  
Coupling Constant ◽  
Renormalization Group Analysis ◽  
Flow Equations ◽  
Interaction Term

A weakly interacting Bose–Fermi mixture model was investigated using Wisonian renormalization group (RG). This model includes one boson–boson interaction term and one boson–fermion interaction term. The scaling dimensions of the two interaction coupling constants were calculated as 2-D at tree level and the flow equations were derived at one-loop level. We find that in the flow equations the contributions from the fermion loops go to zero as the length scale approaches infinity. In three-dimensional case two fixed points are calculated. One is the Gaussian fixed point and the other one is Wilson–Fisher fixed point. We observe that the boson–fermion interaction decouples at the Wilson–Fisher fixed point. We also find that under RG transformation the boson–fermion interaction coupling constant runs to negative infinity with a small negative initial value, which indicates a boson–fermion pairing instability. Furthermore, the possibility of emergent supersymmetry in this model was discussed.

Sign in / Sign up

Export Citation Format

Share Document