Second-order and Fluctuation-induced First-order Phase Transitions with Functional Renormalization Group Equations

Abstract

We investigate phase transitions in scalar field theories using the functional renormalization group (RG) equation. We analyze a system with $U(2)\times U(2)$ symmetry, in which there is a parameter ${\lambda }_2$ that controls the strength of the first-order phase transition driven by fluctuations. In the limit of ${\lambda }_2\to 0$, the $U(2)\times U(2)$ theory is reduced to an $O(8)$ scalar theory that exhibits a second-order phase transition in three dimensions. We develop a new insight for the understanding of the fluctuation-induced first-order phase transition as a smooth continuation from the standard RG flow in the $O(8)$ system. In our view from the RG flow diagram on coupling parameter space, the region that favors the first-order transition emerges from the unphysical region to the physical one as ${\lambda }_2$ increases from zero. We give this interpretation based on the Taylor expansion of the functional RG equations up to the fourth order in terms of the field, which encompasses the $\epsilon$-expansion results. We compare results from the expansion and from the full numerical calculation and find that the fourth-order expansion is only of qualitative use and that the sixth-order expansion improves the quantitative agreement.

15 pages, 10 figures, collapsed expressions in the abstract fixed

References in corpus (25)

• Exact evolution equation for the effective potential
• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The QCD transition temperature: results with physical masses in the continuum limit
• The QCD transition temperature: results with physical masses in the continuum limit II.
• The Phase Structure of the Polyakov--Quark-Meson Model
• The phase structure of the Polyakov--quark-meson model beyond mean field
• Susceptibilities near the QCD (tri)critical point
• 2+1 Flavor Polyakov--Nambu--Jona-Lasinio Model at Finite Temperature and Nonzero Chemical Potential
• The renormalization group and quark number fluctuations in the Polyakov loop extended quark-meson model at finite baryon density
• Ising exponents from the functional renormalisation group
• Three flavor Nambu-Jona Lasinio model with Polyakov loop and competition with nuclear matter
• QCD Thermodynamics from the Lattice
• Beyond the rainbow: effects from pion back-coupling
• The QCD Phase Boundary from Quark-Gluon Dynamics
• On the scaling behavior of the chiral phase transition in QCD in finite and infinite volume
• Non-perturbative thermal flows and resummations
• Non perturbative renormalization group and momentum dependence of n-point functions (II)
• Towards finite density QCD with Taylor expansions
• Perturbation theory and non-perturbative renormalization flow in scalar field theory at finite temperature
• High-accuracy scaling exponents in the local potential approximation
• U_A(1) anomaly and eta' mass from an infrared singular quark-gluon vertex
• Scaling functions for the O(4)-model in d=3 dimensions
• O(N) universality and the chiral phase transition in QCD
• UA(1) breaking and phase transition in chiral random matrix model
• Random matrix model at nonzero chemical potentials with anomaly effects

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• Functional renormalization group study of the two-flavor linear sigma model in the presence of the axial anomaly
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• Fluctuation induced first order phase transition in U(n)xU(n) models using chiral invariant expansion of functional renormalization group flows
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• Invariant formulation of the Functional Renormalisation Group method for $U(n)\times U(n)$ symmetric matrix models
• Fluctuation-induced higher-derivative couplings and infrared dynamics of the Quark-Meson-Diquark Model
• On-shell versus curvature mass parameter fixing schemes in the quark-meson model and its phase diagrams
• Simulating frustrated magnetism with spinor Bose gases
• Chiral symmetry breaking patterns in the U_L(n)xU_R(n) meson model
• Harmonic expansion of the effective potential in Functional Renormalization Group at finite chemical potential
• First-order phase transitions in spinor Bose gases and frustrated magnets
• Solving the QCD non-perturbative flow equation as a partial differential equation and its application to the dynamical chiral symmetry breaking
• Finite temperature symmetry restoration in the U_L(3)xU_R(3) linear sigma model from a large-n approximation
• Nonperturbative Renormalization Group for the Landau-de Gennes Model
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