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 Bootstrapping the $$ \mathcal{N} $$ = 1 Wess-Zumino models in three dimensions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Junchen Rong ◽  
Ning Su
Keyword(s):  
Fixed Point ◽  
Lie Groups ◽  
Permutation Group ◽  
Critical Exponents ◽  
Unitary Group ◽  
Bootstrap Method ◽  
Three Dimensional ◽  
Equation Of Motion ◽  
Three Dimensions ◽  
Scaling Dimension

Abstract Using numerical bootstrap method, we determine the critical exponents of the minimal three-dimensional $$ \mathcal{N} $$ N = 1 Wess-Zumino models with cubic superpotetential $$ \mathcal{W}\sim {d}_{ijk}{\Phi}^i{\Phi}^j{\Phi}^k $$ W ∼ d ijk Φ i Φ j Φ k . The tensor dijk is taken to be the invariant tensor of either permutation group SN, special unitary group SU(N), or a series of groups called F4 family of Lie groups. Due to the equation of motion, at the Wess-Zumino fixed point, the operator dijkΦjΦk is a (super)descendant of Φi. We observe such super-multiplet recombination in numerical bootstrap, which allows us to determine the scaling dimension of the super-field ∆Φ.

scholarly journals THE CASE OF ASYMPTOTIC SUPERSYMMETRY

2013 ◽  
Vol 28 (14) ◽  
pp. 1350053 ◽  
Author(s):  
BRUCE L. SÁNCHEZ-VEGA ◽  
ILYA L. SHAPIRO
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Gauge Coupling ◽  
High Energy ◽  
Systematic Investigation ◽  
Coupling Constants ◽  
Scalar Coupling ◽  
Asymptotic State ◽  
Stable Fixed Point ◽  
Scalar Couplings

We start systematic investigation for the possibility to have supersymmetry (SUSY) as an asymptotic state of the gauge theory in the high energy (UV) limit, due to the renormalization group running of coupling constants of the theory. The answer on whether this situation takes place or not, can be resolved by dealing with the running of the ratios between Yukawa and scalar couplings to the gauge coupling. The behavior of these ratios does not depend too much on whether gauge coupling is asymptotically free (AF) or not. It can be shown that the UV stable fixed point for the Yukawa coupling is not supersymmetric. Taking this into account, one can break down SUSY only in the scalar coupling sector. We consider two simplest examples of such breaking, namely N = 1 supersymmetric QED and QCD. In one of the cases one can construct an example of SUSY being restored in the UV regime.

scholarly journals RENORMALIZATION GROUP FLOW EQUATIONS FOR THE SCALAR O(N) THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 2119-2124 ◽  
Author(s):  
B.-J. SCHAEFER ◽  
O. BOHR ◽  
J. WAMBACH
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Three Dimensions ◽  
Leading Order ◽  
Renormalization Group Flow ◽  
Derivative Expansion ◽  
Scalar Theory ◽  
Flow Equations ◽  
Self Consistent ◽  
Group Flow

Self-consistent new renormalization group flow equations for an O(N)-symmetric scalar theory are approximated in next-to-leading order of the derivative expansion. The Wilson-Fisher fixed point in three dimensions is analyzed in detail and various critical exponents are calculated.

scholarly journals On the Measure-Preserving Mappings with Three-Dimensions

1993 ◽  
Vol 132 ◽  
pp. 73-89
Author(s):  
Yi-Sui Sun
Keyword(s):  
Fixed Point ◽  
Invariant Manifolds ◽  
Three Dimensional ◽  
Invariant Curve ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Kolmogorov Entropy ◽  
Numerical Exploration ◽  
Area Preserving ◽  
Dimensional Mapping

AbstractWe have systematically made the numerical exploration about the perturbation extension of area-preserving mappings to three-dimensional ones, in which the fixed points of area preserving are elliptic, parabolic or hyperbolic respectively. It has been observed that: (i) the invariant manifolds in the vicinity of the fixed point generally don’t exist (ii) when the invariant curve of original two-dimensional mapping exists the invariant tubes do also in the neighbourhood of the invariant curve (iii) for the perturbation extension of area-preserving mapping the invariant manifolds can only be generated in the subset of the invariant manifolds of original two-dimensional mapping, (iv) for the perturbation extension of area preserving mappings with hyperbolic or parabolic fixed point the ordered region near and far from the invariant curve will be destroyed by perturbation more easily than the other one, This is a result different from the case with the elliptic fixed point. In the latter the ordered region near invariant curve is solid. Some of the results have been demonstrated exactly.Finally we have discussed the Kolmogorov Entropy of the mappings and studied some applications.

scholarly journals The cubic fixed point at large N

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Damon J. Binder
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Ising Model ◽  
Ising Models ◽  
Three Dimensions ◽  
Renormalization Group Flow ◽  
Conformal Bootstrap ◽  
Large N ◽  
Group Flow ◽  
3D Ising Model

Abstract By considering the renormalization group flow between N coupled Ising models in the UV and the cubic fixed point in the IR, we study the large N behavior of the cubic fixed points in three dimensions. We derive a diagrammatic expansion for the 1/N corrections to correlation functions. Leading large N corrections to conformal dimensions at the cubic fixed point are then evaluated using numeric conformal bootstrap data for the 3d Ising model.

CRITICAL BEHAVIOR OF A TWO COMPONENT COMPLEX FIELD MODEL AND SYMMETRY OF ITS RENORMALIZATION GROUP STRUCTURE

1996 ◽  
Vol 10 (10) ◽  
pp. 439-449 ◽  
Author(s):  
E.J. BLAGOEVA
Keyword(s):  
Renormalization Group ◽  
Critical Behavior ◽  
Critical Exponents ◽  
Heavy Fermion ◽  
Field Model ◽  
Group Structure ◽  
Complex Field ◽  
Loop Order ◽  
Scaling Properties ◽  
Two Component

The critical behavior of a two-component (n/2=2) complex field model applied to heavy-fermion and high-Tc superconductors is studied by the renormalization group in d=4−∊. Fixed points with new scaling properties are discovered and their critical exponents are presented beyond the two-loop order. A generalization for n/2 >2 carried out.

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