Thermal and Quantum Phase Transitions of the ${\varphi }^4$ Model

Abstract

In this paper we discuss and revisit the finite temperature extension of the renormalization group (RG) treatment of $T=0$ field theories, focusing as a case study on the ${\varphi }^4$ model. We first discuss the extension of RG equations of the very same model from $T=0$ to finite $T$ in the usual way by resorting to sums on the Matsubara frequencies and fixing the physical temperature parameter $T$. We show that this approach, although useful for a variety of applications, may lead to the disappearance of the critical points as extracted from the RG flow. Since the identification of fixed points is key in the study of classical and quantum phase transitions, wepropose a modification of the usual finite-temperature RG approach by relating the temperature parameter to the running RG scale, $T\equiv k_T=\tau k$ where $k_T$ is the running cutoff for thermal, and $k$ is for the quantum fluctuations. Once introduced this dimensionless temperature $\tau$, we investigate the consequences on the thermal RG approach for the ${\varphi }^4$ model and construct its phase diagram. Finally, we formulate requirements for the phase diagram of the ${\varphi }^4$ theory based on known properties of the quantum and classical phase diagrams of the Ising model.

arXiv comment10 pages, 7 figures, final version, to be published in Phys. Rev. D

References in corpus (30)

• Exact evolution equation for the effective potential
• The Exact Renormalisation Group and Approximate Solutions
• Optimisation of the exact renormalisation group
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Chiral phase boundary of QCD at finite temperature
• Confinement from Correlation Functions
• The QCD Phase Boundary from Quark-Gluon Dynamics
• On the Phase Structure of QCD in a Finite Volume
• On the scaling behavior of the chiral phase transition in QCD in finite and infinite volume
• Perturbation theory and non-perturbative renormalization flow in scalar field theory at finite temperature
• Nonperturbative renormalization-group approach to strongly-correlated lattice bosons
• The Effect of Fluctuations on the QCD Critical Point in a Finite Volume
• Non-perturbative renormalization-group approach to the Bose-Hubbard model
• Fierz-complete NJL model study: fixed points and phase structure at finite temperature and density
• Influence of quark boundary conditions on the pion mass in finite volume
• Turning a First Order Quantum Phase Transition Continuous by Fluctuations: General Flow Equations and Application to d-Wave Pomeranchuk Instability
• Test of quantum thermalization in the two-dimensional transverse-field Ising model
• Renormalization group for phases with broken discrete symmetry near quantum critical points
• Thermodynamics in the vicinity of a relativistic quantum critical point in 2+1 dimensions
• Inverse Symmetry Breaking and the Exact Renormalization Group
• Many-flavor Phase Diagram of the (2+1)d Gross-Neveu Model at Finite Temperature
• Higgs Criticality beyond the Standard Model
• Calculation of the pressure of a hot scalar theory within the Non-Perturbative Renormalization Group
• Dimensional regularization, Wilsonian RG, and the Naturalness/Hierarchy problem
• Finite temperature crossovers near quantum tricritical points in metals
• Renormalized phi^6 model for quantum phase transitions in systems of itinerant fermions
• Finite-size and Particle-number Effects in an Ultracold Fermi Gas at Unitarity
• Physical Tuning and Naturalness
• Phase boundary and finite temperature crossovers of the quantum Ising model in two dimensions
• Time Evolution and Thermal Renormalization Group Flow in Cosmology

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