Renormalization-group calculation of critical exponents in three dimensions

1975 ◽  
Author(s):  
G. R. Golner ◽  
E. K. Riedel
Keyword(s):  
Renormalization Group ◽  
Critical Exponents ◽  
Three Dimensions ◽  
Renormalization Group Calculation

Critical Exponents for the Model with Unique Stable Fixed Point From Three-Loop RG Expansions

1998 ◽  
Vol 12 (12n13) ◽  
pp. 1365-1377 ◽  
Author(s):  
A. I. Sokolov ◽  
K. B. Varnashev ◽  
A. I. Mudrov
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Critical Exponents ◽  
Structural Transition ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Flow Diagram ◽  
Stable Fixed Point ◽  
Loop Order ◽  
Symmetry Properties

The critical behavior of a model describing phase transitions in cubic and tetragonal anti-ferromagnets with 2N-component (N>1) real order parameters as well as the structural transition in NbO 2 crystal is studied within the field-theoretical renormalization-group (RG) approach in three and (4-∊)-dimensions. Perturbative expansions for RG functions are calculated up to three-loop order and resummed, in 3D, by means of the generalized Padé–Borel procedure which is shown to preserve the specific symmetry properties of the model. It is found that a stable fixed point does exist in the three-dimensional RG flow diagram for N>1, in accordance with predictions obtained earlier within the ∊-expansion. Fixed-point coordinates and critical-exponent values are presented for physically interesting cases N=2 and N=3. In both cases critical exponents are found to be numerically close to those of the 3DXY model. The analysis of the results given by the ∊-expansion and by the RG approach in three dimensions is performed resulting in a conclusion that the latter provides much more accurate numerical estimates.

Percolation with first- and second-neighbor bonds: Renormalization-group calculation of critical exponents

1980 ◽  
Vol 22 (7) ◽  
pp. 3481-3485 ◽  
Author(s):  
Rosane Riera ◽  
P. Murilo Oliveira ◽  
C. M. Chaves ◽  
S. L. A. de Queiroz
Keyword(s):  
Renormalization Group ◽  
Critical Exponents ◽  
Renormalization Group Calculation
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