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 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

FUNCTIONAL RENORMALIZATION GROUP IN THE 2D HUBBARD MODEL

2006 ◽  
Vol 20 (19) ◽  
pp. 2636-2646 ◽  
Author(s):  
CARSTEN HONERKAMP
Keyword(s):  
Renormalization Group ◽  
Hubbard Model ◽  
Fermi Liquid ◽  
Broken Symmetry ◽  
Two Dimensional ◽  
Functional Renormalization Group ◽  
Recent Developments ◽  
Dimensional Models ◽  
Low Dimensional

We review recent developments in functional renormalization group (RG) methods for interacting fermions. These approaches aim at obtaining an unbiased picture of competing Fermi liquid instabilities in the low-dimensional models like the two-dimensional Hubbard model. We discuss how these instabilities can be approached from various sides and how the fermionic RG flow can be continued into phases with broken symmetry.

QUANTUM BLACK HOLES, STRINGS AND σ-MODELS AT θ=π: HAWKING QUANTUM EVAPORATION AS WORLD-SHEET RG-FLOW

1991 ◽  
Vol 06 (36) ◽  
pp. 3297-3311 ◽  
Author(s):  
IAN I. KOGAN
Keyword(s):  
Black Holes ◽  
Renormalization Group ◽  
Fixed Points ◽  
Quantum Hall ◽  
Conformal Factor ◽  
Two Dimensional ◽  
Stable States ◽  
World Sheet ◽  
Final State ◽  
Quantum Evaporation

We discuss the quantum black holes and even more generally the problem of quantum horizons in string theory. A toy model for quantum horizon is the two-dimensional O(3) σ-model. Using the interpretation of time as zero mode of conformal factor of world-sheet metric (Liouville field) the possible equivalence between two-dimensional renormalization group equations and Hawking quantum evaporation formula is found. The infrared fixed points of two-dimensional renormalization group corresponds to final state of the quantum black hole. Using conjecture that such a fixed points are described by σ-models with θ=π we suggest the axionic black holes as possible candidates to final (meta)stable states of black holes. The corresponding renormalization group picture are similar to the quantum Hall effect.

The renormalization group (RG) approach: The critical theory near four dimensions

2021 ◽  
pp. 357-390
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Fixed Points ◽  
Gaussian Approximation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Flow Equations ◽  
Four Dimensions ◽  
The Mean

In Chapter 14, the singular behavior of ferromagnetic systems with O(N) symmetry and short-range interactions, near a second order phase transition has been determined in the mean-field approximation, which is also a quasi-Gaussian approximation. The mean-field approximation predicts a set of universal properties, properties independent of the detailed structure of the microscopic Hamiltonian, the dimension of space, and, to a large extent, of the symmetry of systems. However, the leading corrections to the mean-field approximation, in dimensions smaller than or equal to four, diverge at the critical temperature, and the universal predictions of the mean-field approximation cannot be correct. Such a problem originates from the non-decoupling of scales and leads to the question of possible universality. In Chapter 9, the question has been answered in four dimensions using renormalization theory, and related renormalization group (RG) equations. Moreover, below four dimensions, in an expansion around the mean-field, the most singular terms near criticality can be also formally recovered from a continuum, low-mass φ4 field theory. More generally, following Wilson, to understand universality beyond the mean-field approximation, it is necessary to build a general renormalization group in the form of flow equations for effective Hamiltonians and to find fixed points of the flow equations. Near four dimensions, the flow equations can be approximated by the renormalization group of quantum field theory (QFT), and the fixed points and critical behaviours derived within the framework of the Wilson-Fisher ϵ expansion.

scholarly journals Four Loop Scalar ϕ4 Theory Using the Functional Renormalization Group

Universe ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 9 ◽  
Author(s):  
Margaret Carrington ◽  
Christopher Phillips
Keyword(s):  
Renormalization Group ◽  
Effective Theory ◽  
Group Method ◽  
Coupling Constant ◽  
Loop Order ◽  
Quartic Coupling ◽  
Scalar Theory ◽  
Functional Renormalization Group ◽  
Bare Coupling Constant ◽  
Effective Theories

We work with a symmetric scalar theory with quartic coupling in 4-dimensions. Using a 2PI effective theory and working at 4 loop order, we renormalize with a renormalization group method. All divergences are absorbed by one bare coupling constant and one bare mass which are introduced at the level of the Lagrangian. The method is much simpler than counterterm renormalization, and can be generalized to higher order nPI effective theories.

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