Static approach to renormalization group analysis of stochastic models with spatially quenched disorder
arXiv:1905.04470 · doi:10.1007/s10955-019-02436-8
Abstract
A new ''static'' renormalization group approach to stochastic models of fluctuating surfaces with spatially quenched noise is proposed in which only time-independent quantities are involved. As examples, quenched versions of the Kardar-Parisi-Zhang model and its Pavlik's modification, the Hwa-Kardar model of self-organized criticality, and Pastor-Satorras-Rothman model of landscape erosion are studied. It is shown that the upper critical dimension in the quenched models is shifted by two units upwards in comparison to their counterparts with white in-time noise. Possible scaling regimes associated with fixed points of the renormalization group equations are found and the critical exponents are derived to the leading order of the corresponding epsilon-expansions. Some exact values and relations for these exponents are obtained.
arXiv comment22 pages
References in corpus (40)
- Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
- Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
- An Introduction to the Nonperturbative Renormalization Group
- Introduction to the functional RG and applications to gauge theories
- Two-Loop Renormalization Group Analysis of the Burgers-Kardar-Parisi-Zhang Equation
- Non-perturbative renormalization group for the Kardar-Parisi-Zhang equation
- SCALING AND INTERMITTENCY IN BURGERS' TURBULENCE
- Critical Dynamics of the Contact Process with Quenched Disorder
- Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications
- Width Distributions and the Upper Critical Dimension of KPZ Interfaces
- Upper critical dimension, dynamic exponent and scaling functions in the mode-coupling theory for the Kardar-Parisi-Zhang equation
- On the Perturbation Expansion of the KPZ-Equation
- On the Renormalization of the Kardar-Parisi-Zhang equation
- General framework of the non-perturbative renormalization group for non-equilibrium steady states
- Mode coupling and renormalization group results for the noisy Burgers equation
- Nonperturbative renormalization group for the stationary Kardar-Parisi-Zhang equation: scaling functions and amplitude ratios in 1+1, 2+1 and 3+1 dimensions
- Fully developed isotropic turbulence: nonperturbative renormalization group formalism and fixed point solution
- Universality of fluctuations in the Kardar-Parisi-Zhang class in high dimensions and its upper critical dimension
- Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark
- Localized growth modes, dynamic textures, and upper critical dimension for the Kardar-Parisi-Zhang equation in the weak noise limit
- The Kardar-Parisi-Zhang equation in the weak noise limit: Pattern formation and upper critical dimension
- Scaling of a slope: the erosion of tilted landscapes
- The Kardar-Parisi-Zhang equation with spatially correlated noise: a unified picture from nonperturbative renormalization group
- Anisotropic Surface Growth Model in Disordered Media
- Continuum Model for River Networks
- Stochastic equation for the erosion of inclined topography
- Upper critical dimension of the KPZ equation
- Fully developed isotropic turbulence: symmetries and exact identities
- Existence of the upper critical dimension of the Kardar-Parisi-Zhang equation
- Disorder-induced critical behavior in driven diffusive systems
- Local minimal energy landscapes in river networks
- Non-universality in the erosion of tilted landscapes
- Scaling in erosion of landscapes: Renormalization group analysis of a model with infinitely many couplings
- Strong-coupling phases of the anisotropic Kardar-Parisi-Zhang equation
- Random interface growth in random environment: Renormalization group analysis of a simple model
- Matrix generalizations of some dynamic field theories
- Scaling in erosion of landscapes: Renormalization group analysis of a model with turbulent mixing
- Patterns in the Kardar-Parisi-Zhang equation
- Effects of random environment on a self-organized critical system: Renormalization group analysis of a continuous model
- "Sinc"-Noise for the KPZ Equation
Cited by in corpus (6)
- Scaling of Entropy Production under Coarse Graining in Active Disordered Media
- Effects of Turbulent Environment and Random Noise on Self-Organized Critical Behavior: Universality vs Nonuniversality
- Effects of turbulent environment on self-organized critical behavior: Isotropy vs Anisotropy
- Stirred Kardar-Parisi-Zhang equation with quenched random noise: Emergence of induced nonlinearity
- Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment
- Effect of random environment on kinetic roughening: Kardar-Parisi-Zhang model with a static noise coupled to the Navier-Stokes equation