Fluctuation Induced Critical Behavior at Non-Zero Temperature and Chemical Potential

Abstract

We discuss phase transitions in relativistic systems as a function of both chemical potential and temperature. The presence of a chemical potential explicitly breaks Lorentz invariance and may additionally break other internal symmetries. This introduces new subtleties in the determination of the critical properties. We discuss separately three characteristic effects of a nonzero chemical potential. Firstly, we consider only the explicit breaking of Lorentz invariance using a scalar field theory with a global U(1) symmetry. Secondly, we study the explicit breaking of an internal symmetry in addition to Lorentz invariance using two--color QCD at nonzero baryonic chemical potential. Finally, we consider the spontaneous breaking of a symmetry using three-color QCD at nonzero baryonic and isospin chemical potential. For each case, we derive the appropriate three-dimensional effective theory at criticality and study the effect of the chemical potential on the fixed point structure of the $\beta$-functions. We find that the order of the phase transition is not affected by the explicit breaking of Lorentz invariance but is sensitive to the breaking of additional symmetries by the chemical potential.

latex, 11 page, 1 figure, 1 table. Clarifications and one ref added. Version to appear in PRD

References in corpus (22)

• QCD at finite isospin density
• QCD-like Theories at Finite Baryon Density
• Lattice QCD at finite isospin density at zero and finite temperature
• On two-color QCD with baryon chemical potential
• Imaginary chemical potential and finite fermion density on the lattice
• QCD at finite isospin density: from pion to quark-antiquark condensation
• QCD-like Theories at Finite Baryon and Isospin Density
• The superfluid phases of quark matter: Ginzburg-Landau theory and color neutrality
• QCD at small non-zero quark chemical potentials
• Quenched lattice QCD at finite isospin density and related theories
• Superfluid phases of quark matter. III. Supercurrents and vortices
• Diquark Condensate in QCD with Two Colors at Next-to-Leading Order
• Thermodynamics of chiral symmetry at low densities
• The Superfluid and Conformal Phase Transitions of Two-Color QCD
• The Ginzburg-Landau Free Energy Functional of Color Superconductivity at Weak Coupling
• The $\epsilon$-expansion and the electroweak phase transition
• Superfluid phases of quark matter, II: Phenomenology and sum rules
• On the QCD Phase Transition at Finite Baryon Density
• Chiral Symmetry in Two-Color QCD at Finite Temperature
• Melting the Diquark Condensate in Two-Color QCD: A Renormalization Group Analysis
• Dynamics near the critical point: the hot renormalization group in quantum field theory
• Color-SU(3)-Ginzburg-Landau Effective Potential for Order Parameter with $3\times 3$ Symmetry