The Symmetry and Renormalization Group Fixed Points of Quartic Hamiltonians

1984 ◽  
pp. 63-92 ◽  
Author(s):  
Louis Michel
Keyword(s):  
Renormalization Group ◽  
Fixed Points

PERTURBED W3 CONFORMAL THEORIES AND SPIN-4/3 PARAFERMIONIC COSET MODELS

1991 ◽  
Vol 06 (25) ◽  
pp. 2281-2287 ◽  
Author(s):  
R. B. MANN ◽  
H. B. ZHENG
Keyword(s):  
Renormalization Group ◽  
Fixed Points ◽  
Renormalization Group Flows ◽  
Coset Models

Renormalization group flows in W3, conformal theories are analyzed in relation to the ones in spin-4/3 parafermionic coset models and some of the operator content for new fixed points is identified.

Fixed points of renormalization group for the hierarchical fermionic model

1994 ◽  
Vol 76 (3-4) ◽  
pp. 805-817 ◽  
Author(s):  
E. Yu. Lerner ◽  
M. D. Missarov
Keyword(s):  
Renormalization Group ◽  
Fixed Points ◽  
Fermionic Model

Stability of renormalization group fixed points and decay of correlations

2019 ◽  
pp. 101-110
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Fixed Points ◽  
Gradient Flow ◽  
Scalar Fields ◽  
Effective Field ◽  
Coupling Constants ◽  
Critical Systems ◽  
Universal Properties ◽  
General Physical

Chapter 7 is devoted to a discussion of the renormalization group (RG) flow when the effective field theory that describes universal properties of critical phenomena depends on several coupling constants. The universal properties of a large class of macroscopic phase transitions with short range interactions can be described by statistical field theories involving scalar fields with quartic interactions. The simplest critical systems have an O(N) orthogonal symmetry and, therefore, the corresponding field theory has only one quartic interaction. However, in more general physical systems, the flow of quartic interactions is more complicated. This chapter examines these systems from the RG viewpoint. RG beta functions are shown to generate a gradient flow. Some examples illustrate the notion of emergent symmetry. The local stability of fixed points is related to the value of the scaling field dimension.

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.

Renormalization group fixed points in Yukawa theories

1975 ◽  
Vol 93 (1) ◽  
pp. 165-175 ◽  
Author(s):  
D. Bailin ◽  
A. Love ◽  
G. Spathis
Keyword(s):  
Renormalization Group ◽  
Fixed Points

GENERALIZED COULOMB GAS MODELS WITH EXPONENTIAL INTERACTIONS AND A SERIES OF CENTRAL CHARGES

1991 ◽  
Vol 06 (12) ◽  
pp. 2189-2211
Author(s):  
MYUNG-HOON CHUNG
Keyword(s):  
Renormalization Group ◽  
Vector Field ◽  
Fixed Points ◽  
Root Systems ◽  
Coulomb Gas ◽  
Renormalization Group Flow ◽  
Geometrical Figure ◽  
Fermionic Fields ◽  
Background Charge ◽  
Group Flow

The renormalization of the generalized Coulomb gas model with exponential interactions is studied. This model contains a bosonic vector field and several fermionic fields in the presence of a background charge vector. It is shown that the vectors associated with the exponential interactions should satisfy certain conditions for the action to be renormalizable. The conditions require the vectors to form a geometrical figure. In particular, models are considered where the vectors are root systems which form equilateral geometrical figures. Explicit β-functions are obtained for these models. They show several nontrivial fixed points at which the central charges of the system are evaluated. It is found that a renormalization group flow connects the extremal nontrivial fixed points. Some possible applications are indicated.

scholarly journals Nonthermal fixed points and the functional renormalization group

2009 ◽  
Vol 813 (3) ◽  
pp. 383-407 ◽  
Author(s):  
Jürgen Berges ◽  
Gabriele Hoffmeister
Keyword(s):  
Renormalization Group ◽  
Fixed Points ◽  
Functional Renormalization Group

scholarly journals SOLUTIONS OF THE POLCHINSKI ERG EQUATION IN THE O(N) SCALAR MODEL

2002 ◽  
Vol 17 (32) ◽  
pp. 4871-4902 ◽  
Author(s):  
YU. A. KUBYSHIN ◽  
R. NEVES ◽  
R. POTTING
Keyword(s):  
Renormalization Group ◽  
Fixed Points ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Scalar Model ◽  
Regular Solutions ◽  
Exact Renormalization Group

Solutions of the Polchinski exact renormalization group equation in the scalar O(N) theory are studied. Families of regular solutions are found and their relation with fixed points of the theory is established. Special attention is devoted to the limit N = ∞, where many properties can be analyzed analytically.

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