Effects of Turbulent Environment and Random Noise on Self-Organized Critical Behavior: Universality vs Nonuniversality

Abstract

Self-organized criticality in the Hwa-Kardar model of "running sandpile" [Phys. Rev. A 45, 7002 (1992)] with a turbulent motion of the environment taken into account is studied with the field theoretic renormalization group (RG). The turbulent flow is modelled by the synthetic $d$-dimensional anisotropic velocity ensemble introduced by Avellaneda and Majda [Commun. Math. Phys.131: 381 (1990)] with finite correlation time. The Hwa-Kardar model with time-independent (spatially quenched) random noise is considered alongside the original model with the white noise. The aim of the present paper is to explore fixed points of RG equations which determine the possible types of universality classes (regimes of critical behavior of the system) and critical dimensions of the measurable quantities. Our calculations demonstrate that influence of the type of the random noise is extremely large: in contrast to the case of the white noise where the system possess three fixed points, the case of the spatially quenched noise involves four fixed points with overlapping stability regions. This means that in the latter case the critical behavior of the system depends not only on the global parameters of the system which is the usual case, but also on the initial values of the charges (coupling constants) of the system. These initial conditions determine the specific fixed point which will be reached by RG flow. Since now the critical properties of the system are not defined strictly by its parameters the situation may be interpreted as universality violation. Such systems are not forbidden but they are very rare. It is especially interesting that the same model without turbulent motion of the environment does not predict this nonuniversal behavior and demonstrates the "usual" one with prescribed universality classes instead [J.~Stat. Phys. 178, 392 (2020)].

arXiv comment21 pages, 6 figures. V2 is the version accepted for publication

References in corpus (44)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Particles and fields in fluid turbulence
• Are biological systems poised at criticality?
• Dynamical synapses causing self-organized criticality in neural networks
• Colloquium: Criticality and dynamical scaling in living systems
• Power laws and Self-Organized Criticality in Theory and Nature
• 25 Years of Self-Organized Criticality: Concepts and Controversies
• Critical Dynamics of the Contact Process with Quenched Disorder
• Anomalous scaling regimes of a passive scalar advected by the synthetic velocity field
• The mechanisms of self-organised criticality in social processes of knowledge creation
• Anomalous scaling of a passive scalar advected by the synthetic compressible flow
• Turbulence with Pressure: Anomalous Scaling of a Passive Vector Field
• An exact mapping of the stochastic field theory for Manna sandpiles to interfaces in random media
• Growing Critical: Self-Organized Criticality in a Developing Neural System
• Anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time: Two-loop approximation
• Can Renormalization Group Flow End in a Big Mess?
• Coherent-state path integral versus coarse-grained effective stochastic equation of motion: From reaction diffusion to stochastic sandpiles
• Scaling of a slope: the erosion of tilted landscapes
• Anisotropic Surface Growth Model in Disordered Media
• Stochastic equation for the erosion of inclined topography
• Effects of mixing and stirring on the critical behavior
• Effects of turbulent mixing on the nonequilibrium critical behaviour
• Passive advection of a vector field: Anisotropy, finite correlation time, exact solution and logarithmic corrections to ordinary scaling
• Disorder-induced critical behavior in driven diffusive systems
• Critical behaviour of a fluid in a random shear flow: Renormalization group analysis of a simplified model
• Logarithmic violation of scaling in strongly anisotropic turbulent transfer of a passive vector field
• Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models
• Effects of turbulent transfer on the critical behaviour
• Non-universality in the erosion of tilted landscapes
• Self-Organised Criticality and Emergent Hyperbolic Networks -- Blueprint for Complexity in Social Dynamics
• Scaling in erosion of landscapes: Renormalization group analysis of a model with infinitely many couplings
• Faceted patterns and anomalous surface roughening driven by long-term correlated noise
• Random interface growth in random environment: Renormalization group analysis of a simple model
• Inertial-range behaviour of a passive scalar field in a random shear flow
• Scaling in erosion of landscapes: Renormalization group analysis of a model with turbulent mixing
• Hydrodynamics, density fluctuations and universality in conserved stochastic sandpiles
• Static approach to renormalization group analysis of stochastic models with spatially quenched disorder
• Collective emotion dynamics in chats with agents, moderators and Bots
• Effects of random environment on a self-organized critical system: Renormalization group analysis of a continuous model
• Effects of turbulent environment on self-organized critical behavior: Isotropy vs Anisotropy
• Effects of Turbulent Mixing on the Critical Behavior
• Ito and Stratonovich calculuses in stochastic field theory
• Critical behaviour of the randomly stirred dynamical Potts model: Novel universality class and effects of compressibility
• Effects of turbulent mixing on critical behaviour: Renormalization group analysis of the Potts model

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