scholarly journals Functional renormalization group for commensurate antiferromagnets: Beyond the mean-field picture

2014 ◽  
Vol 90 (3) ◽  
Author(s):  
Stefan A. Maier ◽  
Andreas Eberlein ◽  
Carsten Honerkamp
Keyword(s):  
Renormalization Group ◽  
Mean Field ◽  
Functional Renormalization Group ◽  
The Mean

scholarly journals Angle-resolved study of density waves, superconductivity and pseudogap in two dimensions

2002 ◽  
Vol 12 (9) ◽  
pp. 65-68
Author(s):  
D. Zanchi
Keyword(s):  
Renormalization Group ◽  
Mean Field ◽  
Two Dimensions ◽  
Square Lattice ◽  
Correlated Electrons ◽  
Functional Renormalization Group ◽  
Half Filling ◽  
The Mean ◽  
Critical Scale ◽  
D Wave

Weakly correlated electrons on a square lattice are studied by angle-resolved functional renormalization group. Upon renormalization the interaction starts to depend on monienta and has pole-like solutions near the doping-dependent critical scale. Near half-filling this critical scale is the pseudogap temperature T*. In the overdoped regime the critical scale is the mean-field like critical temperature for d-wave superconductivity.

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

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.

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.

MEAN FIELD RENORMALIZATION GROUP FOR ISING MODELS WITH S≥1

1996 ◽  
Vol 10 (22) ◽  
pp. 1067-1076 ◽  
Author(s):  
D. PEÑA LARA ◽  
J.A. PLASCAK
Keyword(s):  
Renormalization Group ◽  
Mean Field ◽  
Finite Size ◽  
Ising Models ◽  
Mean Value ◽  
Transition Line ◽  
Present Formalism ◽  
Second Order Transition ◽  
The Mean ◽  
Field Renormalization

The mean field renormalization group is extended in order to study spin-S Ising models (S≥1) by introducing additional parameters in the Hamiltonians of the clusters, in the same spirit as the mean field approach. These new parameters are then consistently obtained according to finite size scaling ideas and quite good results are obtained, even for the smallest choice of the clusters. Moreover, the mean value of the square of the spin along the second-order transition line can also be obtained from the present formalism.

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