Critical Behavior and Dimension Crossover of Pion Superfluidity

Abstract

We investigate the critical behavior of pion superfluidity in the frame of functional renormalization group. By solving the flow equation in the SU(2) linear sigma model with pion superfluidity at finite temperature and isospin density, and making comparison with the fixed point analysis of the flow diagram in a general $O(N)$ model at zero temperature and density but with continuous dimension, the pion superfluidity is a second order phase transition subject to a $O(2)$ universality class with a dimension crossover from $d_{\text{eff}}=4$ to $d_{\text{eff}}=3$. The usually used large $N$ expansion gives a temperature independent critical exponent $\beta$ and agrees with the renormalization group only at zero temperature.

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• Meson Spectral Functions at Finite Temperature and Isospin Density with Functional Renormalization Group
• Baryon number fluctuations in the 2+1 flavor low energy effective model
• Baryon number probability distribution at finite temperature
• Pion condensation in a soft-wall AdS/QCD model
• QCD phase diagram at finite isospin chemical potential and temperature in an IR-improved soft-wall AdS/QCD model
• Four-fermion interactions and the chiral symmetry breaking in an external magnetic field
• Chiral criticality and glue dynamics
• FRG analysis for a relativistic BEC in arbitrary spatial dimensions