From quantum to classical dynamics: The relativistic $O(N)$ model in the framework of the real-time functional renormalization group

Abstract

We investigate the transition from unitary to dissipative dynamics in the relativistic $O(N)$ vector model with the $\lambda ({\phi }^2{)}^2$ interaction using the nonperturbative functional renormalization group in the real-time formalism. In thermal equilibrium, the theory is characterized by two scales, the interaction range for coherent scattering of particles and the mean free path determined by the rate of incoherent collisions with excitations in the thermal medium. Their competition determines the renormalization group flow and the effective dynamics of the model. Here we quantify the dynamic properties of the model in terms of the scale-dependent dynamic critical exponent $z$ in the limit of large temperatures and in $2\le d\le 4$ spatial dimensions. We contrast our results to the behavior expected at vanishing temperature and address the question of the appropriate dynamic universality class for the given microscopic theory.

32 pages, 12 captioned figures; revised and extended version accepted for publication in PRD

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Cited by in corpus (23)

• The nonperturbative functional renormalization group and its applications
• Thermodynamic Equilibrium as a Symmetry of the Schwinger-Keldysh Action
• Real time correlation functions and the functional renormalisation group
• QCD at finite temperature and density within the fRG approach: An overview
• The dynamic critical exponent $z$ of the three-dimensional Ising universality class: Monte Carlo simulations of the improved Blume-Capel model
• Spectral functions and critical dynamics of the $O(4)$ model from classical-statistical lattice simulations
• Spectral functions and dynamic critical behavior of relativistic $Z_2$ theories
• Self-consistent Spectral Functions in the $O(N)$ Model from the FRG
• Spectral functions from the real-time functional renormalization group
• Flowing with the Temporal Renormalisation Group
• The dynamic critical exponent $z$ for 2d and 3d Ising models from five-loop $\epsilon$ expansion
• Thermodynamics of the two-dimensional XY model from functional renormalization
• Real-time dynamics of the $O(4)$ scalar theory within the fRG approach
• Real-time methods for spectral functions
• Model A of critical dynamics: 5-loop $\epsilon$ expansion study
• Self-consistent $O(4)$ model spectral functions from analytically continued FRG flows
• Quantum renormalization group
• Critical Casimir forces from the equation of state of quantum critical systems
• Dissipation dynamics of a scalar field
• Thermal critical dynamics from equilibrium quantum fluctuations
• Self-dual criticality in three-dimensional ${\mathbb{Z}}_2$ gauge theory with matter
• Nonperturbative treatment of a quenched Langevin field theory
• Many-body constraints and non-thermal behavior in 1D open systems with Haldane exclusion statistics