scholarly journals Renormalization group analysis of the three-dimensional Gross–Neveu model at finite temperature and density

2003 ◽  
Vol 567 (1-2) ◽  
pp. 31-38 ◽  
Author(s):  
Paolo Castorina ◽  
Marco Mazza ◽  
Dario Zappalà
Keyword(s):  
Renormalization Group ◽  
Finite Temperature ◽  
Group Analysis ◽  
Three Dimensional ◽  
Renormalization Group Analysis ◽  
Gross Neveu Model

scholarly journals ONE-LOOP RENORMALIZATION GROUP ANALYSIS OF BOSE–FERMI MIXTURES

2012 ◽  
Vol 26 (32) ◽  
pp. 1250197
Author(s):  
BOYANG LIU ◽  
JIANGPING HU
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Group Analysis ◽  
Three Dimensional ◽  
Coupling Constants ◽  
Tree Level ◽  
Coupling Constant ◽  
Renormalization Group Analysis ◽  
Flow Equations ◽  
Interaction Term

A weakly interacting Bose–Fermi mixture model was investigated using Wisonian renormalization group (RG). This model includes one boson–boson interaction term and one boson–fermion interaction term. The scaling dimensions of the two interaction coupling constants were calculated as 2-D at tree level and the flow equations were derived at one-loop level. We find that in the flow equations the contributions from the fermion loops go to zero as the length scale approaches infinity. In three-dimensional case two fixed points are calculated. One is the Gaussian fixed point and the other one is Wilson–Fisher fixed point. We observe that the boson–fermion interaction decouples at the Wilson–Fisher fixed point. We also find that under RG transformation the boson–fermion interaction coupling constant runs to negative infinity with a small negative initial value, which indicates a boson–fermion pairing instability. Furthermore, the possibility of emergent supersymmetry in this model was discussed.

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