Transitions and modulated phases in centrosymmetric ferroelectrics: Mean-field and renormalization-group predictions

1988 ◽  
Vol 37 (4) ◽  
pp. 2133-2155 ◽  
Author(s):  
George A. Hinshaw ◽  
Rolfe G. Petschek
Keyword(s):  
Renormalization Group ◽  
Mean Field ◽  
Modulated Phases

Some exact results from the mean field renormalization group

1992 ◽  
Vol 189 (1-2) ◽  
pp. 367-376 ◽  
Author(s):  
A. das Neves ◽  
J. Kamphorst Leal da Silva ◽  
J.A. Plascak
Keyword(s):  
Renormalization Group ◽  
Mean Field ◽  
Exact Results ◽  
The Mean ◽  
Field Renormalization

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.

FLUCTUATION EFFECTS IN A CLASS OF SYSTEMS WITH TWO ORDER PARAMETERS

1993 ◽  
Vol 07 (27) ◽  
pp. 1725-1731 ◽  
Author(s):  
L. DE CESARE ◽  
I. RABUFFO ◽  
D.I. UZUNOV
Keyword(s):  
Phase Transition ◽  
Renormalization Group ◽  
Phase Transitions ◽  
Order Phase Transition ◽  
Mean Field ◽  
Ising Models ◽  
Order Parameters ◽  
The Mean ◽  
Fluctuation Effects ◽  
Second Order Phase Transition

The phase transitions described by coupled spin -1/2 Ising models are investigated with the help of the mean field and the renormalization group theories. Results for the type of possible phase transitions and their fluctuation properties are presented. A fluctuation-induced second-order phase transition is predicted.

MEAN-FIELD RENORMALIZATION GROUP: BIBLIOGRAPHY AND NEW APPLICATIONS USING LARGE CLUSTERS

1993 ◽  
Vol 07 (10) ◽  
pp. 699-709 ◽  
Author(s):  
K. CROES ◽  
J. O. INDEKEU
Keyword(s):  
Renormalization Group ◽  
Mean Field ◽  
Lattice Models ◽  
Group Methods ◽  
Bulk Surface ◽  
Complete Bibliography ◽  
Large Clusters ◽  
New Applications ◽  
Mean Field Approximations ◽  
Field Renormalization

Renormalization group recursions based on mean-field approximations [J. O. Indekeu, A. Maritan, and A. L. Stella, J. Phys.A15, L291 (1982)], commonly referred to as mean-field renormalization group methods (MFRG), have proven to be efficient and easily applicable for computing non-classical critical properties of lattice models. We give a fairly complete bibliography of applications to date, and extend previous test calculations of bulk, surface, and corner critical exponents in the two-dimensional Ising model to larger cluster sizes on triangular, square (including crossing bonds), and honeycomb lattices. Without much effort the exact value of the critical exponent ratioyH/yT is reproduced systematically with a precision of 2%. This ratio turns out to be the most accurate probe of non-classical critical behaviour that is available in the MFRG method.

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