THE NEW MEAN FIELD RENORMALIZATION GROUP FROM EFFECTIVE FIELD THEORY

1995 ◽  
Vol 09 (24) ◽  
pp. 1617-1621 ◽  
Author(s):  
F. O. COELHO ◽  
J. A. PLASCAK
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Effective Field Theory ◽  
Order Parameter ◽  
Mean Field ◽  
Previous Treatment ◽  
Field Approximation ◽  
Effective Field ◽  
Mean Field Approximation ◽  
Field Renormalization

The new mean field renormalization group is used to study the Ising model through the calculation of the order parameter by means of the effective field theory based on Callen–Suzuki identity. By considering one- and two-spin clusters, better results are obtained when compared to the previous treatment using the usual mean field approximation.

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 Renormalization Group evolution from on-shell SMEFT

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Minyuan Jiang ◽  
Teng Ma ◽  
Jing Shu
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
High Dimensional ◽  
Anomalous Dimensions ◽  
The Standard Model ◽  
Group Evolution

Abstract We describe the on-shell method to derive the Renormalization Group (RG) evolution of Wilson coefficients of high dimensional operators at one loop, which is a necessary part in the on-shell construction of the Standard Model Effective Field Theory (SMEFT), and exceptionally efficient based on the amplitude basis in hand. The UV divergence is obtained by firstly calculating the coefficients of scalar bubble integrals by unitary cuts, then subtracting the IR divergence in the massless bubbles, which can be easily read from the collinear factors we obtained for the Standard Model fields. Examples of deriving the anomalous dimensions at dimension six are presented in a pedagogical manner. We also give the results of contributions from the dimension-8 H4D4 operators to the running of V+V−H2 operators, as well as the running of B+B−H2D2n from H4D2n+4 for general n.

scholarly journals Renormalization group consistency and low-energy effective theories

2019 ◽  
Vol 6 (5) ◽  
Author(s):  
Jens Braun ◽  
Marc Leonhardt ◽  
Jan M. Pawlowski
Keyword(s):  
Renormalization Group ◽  
Mean Field ◽  
Bound State ◽  
Field Approximation ◽  
Low Energy ◽  
Mean Field Approximation ◽  
Quantum Field Theories ◽  
Model Calculations ◽  
Effective Models ◽  
Effective Theories

Low-energy effective theories have been used very successfully to study the low-energy limit of QCD, providing us with results for a plethora of phenomena, ranging from bound-state formation to phase transitions in QCD. These theories are consistent quantum field theories by themselves and can be embedded in QCD, but typically have a physical ultraviolet cutoff that restricts their range of validity. Here, we provide a discussion of the concept of renormalization group consistency, aiming at an analysis of cutoff effects and regularization-scheme dependences in general studies of low-energy effective theories. For illustration, our findings are applied to low-energy effective models of QCD in different approximations including the mean-field approximation. More specifically, we consider hot and dense as well as finite systems and demonstrate that violations of renormalization group consistency affect significantly the predictive power of the corresponding model calculations.

scholarly journals Kinetic field theory: Non-linear cosmic power spectra in the mean-field approximation

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Matthias Bartelmann ◽  
Johannes Dombrowski ◽  
Sara Konrad ◽  
Elena Kozlikin ◽  
Robert Lilow ◽  
...  
Keyword(s):  
Field Theory ◽  
Power Spectrum ◽  
Mean Field ◽  
Power Spectra ◽  
Field Approximation ◽  
Density Fluctuations ◽  
Mean Field Approximation ◽  
Non Linear ◽  
Two Parameters ◽  
Kinetic Field

We use the recently developed Kinetic Field Theory (KFT) for cosmic structure formation to show how non-linear power spectra for cosmic density fluctuations can be calculated in a mean-field approximation to the particle interactions. Our main result is a simple, closed and analytic, approximate expression for this power spectrum. This expression has two parameters characterising non-linear structure growth which can be calibrated within KFT itself. Using this self-calibration, the non-linear power spectrum agrees with results obtained from numerical simulations to within typically \lesssim10\,\%≲10% up to wave numbers k\lesssim10\,h\,\mathrm{Mpc}^{-1}k≲10hMpc−1 at redshift z = 0z=0. Adjusting the two parameters to optimise agreement with numerical simulations, the relative difference to numerical results shrinks to typically \lesssim 5\,\%≲5%. As part of the derivation of our mean-field approximation, we show that the effective interaction potential between dark-matter particles relative to Zel’dovich trajectories is sourced by non-linear cosmic density fluctuations only, and is approximately of Yukawa rather than Newtonian shape.

scholarly journals NATURALNESS IN AN EFFECTIVE FIELD THEORY FOR NEUTRON STAR MATTER

2004 ◽  
Vol 13 (07) ◽  
pp. 1413-1418 ◽  
Author(s):  
MOISÉS RAZEIRA ◽  
CÉSAR A. Z. VASCONCELLOS
Keyword(s):  
Field Theory ◽  
Neutron Stars ◽  
Nuclear Matter ◽  
Effective Field Theory ◽  
Mean Field ◽  
Effective Field ◽  
Hadronic Matter ◽  
Model Parameters ◽  
Static Properties ◽  
Naive Dimensional Analysis

High density hadronic matter is studied in a generalized relativistic multi-baryon Lagrangian density mean field approach which contains nonlinear couplings of the σ, ω, ϱ fields. We compare the predictions of our model with estimates obtained within a phenomenological naive dimensional analysis based on the naturalness of the coefficients of the theory. Upon adjusting the model parameters to describe bulk static properties of ordinary nuclear matter, we show that our approach represents a natural modelling of nuclear matter under the extreme conditions of density as the ones found in the interior of neutron stars. Moreover, we show that naturalness play a major role in effective field theory and, in combination with experiment, could represent a relevant criterium to select a model among others in the description of global static properties of neutron stars.

scholarly journals Effective field theory and nuclear mean-field models

2000 ◽  
Vol 663-664 ◽  
pp. 513c-516c ◽  
Author(s):  
R.J. Furnstahl ◽  
Brian D. Serot
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Mean Field ◽  
Effective Field ◽  
Mean Field Models

A MEAN FIELD STUDY OF THE PHASE TRANSITIONS IN A CLASS OF SYSTEMS WITH COMPLEX ORDER PARAMETERS

1994 ◽  
Vol 08 (28) ◽  
pp. 3963-3986
Author(s):  
EVGENIA J. BLAGOEVA
Keyword(s):  
Phase Diagram ◽  
Phase Transitions ◽  
Order Parameter ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Unconventional Superconductors ◽  
Complex Order ◽  
The Mean ◽  
Expansion Coefficients

A generalized Landau free energy for a complex order parameter expanded up to sixth-order is investigated using group theoretical arguments and the mean-field approximation. Results for the phase transitions that occur are presented. The phase diagram for all allowed values of the expansion coefficients is constructed with an emphasis placed on the influence of the anisotropy in the order parameter space. The results can be used in discussions of unconventional superconductors and modulated structural and magnetic orderings.

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